# How to sketch graph of

9,913 results, page 75

1. ### Calculus check

A function f(x) is continuous for all x and has a local minimum at (1,8). Which must be true? A. f'(1)=0 B. f' exists at x=1 C. The graph is concave up at x=1 D. f'(x) is less than 0 if x is less than 1, f'(x) is greater than 0 if x is greater than 1 E. f'(x) is greater than 0...
2. ### Algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 how would I solve this?
3. ### Algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 how would I solve this?
4. ### Math

1. Find all complex numbers z such that |z-1|=|z+3|=|z-i|, if i is the square root of -1. I got to the part where you graph the equations, but got stuck. 2. Find all cube roots of 8i. I know there are 3 answers, but I am stuck.
5. ### Algebra2

A wave is modeled with the function y = 1/2 sin 3Θ, where Θ is in radius. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis. My answers are Amplitude = 1/2 Period = 2pi/3 Intersection= (0,0), (π/3,0) and (2π/3,0)
6. ### Math

How would you tell if an equation is a funtion or not. I know that it has to have only one y-value for every x...but how do you identify this in an equation (rather than a graph) ie. y=1/2x-7 (how do i tell if this is a funtion or not)? Any help would be much appreciated :)
7. ### Calculus

If f(x)=[x−1/(1+5 x)], there are two points on the graph of y=f(x) at which the tangent lines are parallel to the line x−2y=2. Type in the x values of these points. Type the smaller number first, then the larger number.
8. ### Calculus

If f(x)=[(x−1)/(1+5x)], there are two points on the graph of y=f(x) at which the tangent lines are parallel to the line x−2y=2. Type in the x values of these points. Type the smaller number first, then the larger number.
9. ### Math

Determine whether the given equation is a circle, a point, or a contradiction (no real graph). x^2 + y^2 - 2 x - 16 y + 52 = 0 . The equation is a . (Enter "circle", "point", or "contradiction" in the answer space without quotes.)
10. ### Dependent and Independent variables

Use the equation y=2x+2 for this problem. a. Create an input/output table. b. Graph the ordered pairs from the table. c. Describe each of the variables as the independent or the dependent variable
11. ### physics

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 65.0ú. Dog " A" exerts a force of 256 N and dog " B " exerts a force of 344 N . I) Find the magnitude of the resultant force. ( Answered = 508 N ) II) Find the angle the resultant force ...
12. ### Algebra Help

You are going to write a fairy tale! Your story should include all of the standard elements of fairy tales. Begins “Once upon a time … ” Animals can act like humans. Involves magical items or helpers. Ends “ … happily ever after.” Your story must also fully cover ...
13. ### math

Use the graph, showing the yearly food costs of a family. What was the percent decrease in the cost of food from 2003 to 2004? Your answer must be a percentage. 2003 is 10,500 and 2004 is 9,500
14. ### Algebra

Hi, Any help on this would be very much appreciated. The graph y=3x^2+6x+9 is a parabola, I need to use algebra to find the equation of the axis of symmetry, I then need to use this information to find the coordinates of the vertex. Any ideas? Many thanks
15. ### calculus

An object is moving along the graph of f (x)= x2 . When it reaches the point (2,4) the x coordinate of the object is decreasing at the rate of 3 units/sec. Give the rate of change of the distance between the object and the point (0,1) at the instant when the object is at (2,4).
16. ### Algebra 1

A line passes through (4,2) and is parallel to the graph of x= -3. What equation represents the line in slope-intercept form? It doesn't give me enough information to turn it into slope-intercept form. HELP ME PLEASE!!??!!
17. ### College Algebra

Find the equation of the parabola y = ax2 + bx + c that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola. (−2, −15), (−1, −4), (1/2,-10) y=?
18. ### Math/Algebra

Delivery company charges \$10 plus 40¢ per kilometer or part of a kilometer. Find the cost for a trip of: a.5 kilometers b.7.5 kilometers c.3.2 kilometers d.Graph the ordered pairs (kilometers, cost). Is this a function?
19. ### calculus

5. Find the equation of the tangent line to the graph of f(a) = -sec(a) at the point (0, -1) 6. Differentiate y = sin(x)tan(x). 7. Find f '(x) for f(x) = sin(x)cot(x). 8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex.
20. ### physics

If the relationship between the manipulated variable and the responding variable is an inverse proportion, what will a line graph of this relationship look like? A. a straight line B. a curved line C. a jagged line D. none of the above B?
21. ### Math

Let's say I had a graph for some experiment that we thought was modelled by a = bcd + g. If we perform an experiment and plot a vs. c, what do we expect the slope and intercept to be? Would intercept = g and slope = b ? If that's right, what would d represent?
22. ### 2 problems---math

1. find the relationship of x and y in the table. x: 2; 4; 6; 8; 10 y: 1.5; 2; 3; 4.5; 5 y = _______ x + ________ 2. find the relationship of x and y from a graph of a line that crosses the y-axis at y = 6 and that goes into the left 2 units and rises 3 units. y = _______ x + ...
23. ### math math

Given the linear equation , find the y-coordinates of the points (-6, ), (-3, ), and (3, ). Please show all of your work. Plot those points and graph the linear equation.
24. ### math math

Given the linear equation y=2/3x+1, find the y-coordinates of the points (-6, ), (-3, ), and (3, ). Please show all of your work. Plot those points and graph the linear equation
25. ### algebra

Can someone please explain What polynomial has a graph that passes through the given points? (–4, 89), (–3, 7), (–1, –1), (1, –1), (4, 329) y = 2x3 – 3x2 – 2x + 1 y = 1x4 – 2x3 – 3x2 + 2x + 1 y = x4 – 2x3 + 3x2 + 2x – 1 y = x4 + 2x3 – 3x2 – 2x + 1

Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a)  =  − 4 + 3 , 0 ≤  ≤ 3 b)  =  − 1 , 0 ≤  ≤ 2

Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a) f(x) = x^2 − 4x + 3 , 0 ≤ x ≤ 3 b) f(x) = (x − 1)^2 , 0 ≤ x ≤ 2

Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a) f(x) = x^2 − 4x + 3 , 0 ≤ x ≤ 3 b) f(x) = (x − 1)^2 , 0 ≤ x ≤ 2

Determine the absolute extrema of each function on the given interval. Illustrate your results by sketching the graph of each function. a) f(x) = x^2 − 4x + 3 , 0 ≤ x ≤ 3 b) f(x) = (x − 1)^2 , 0 ≤ x ≤ 2
30. ### math

A graph is given with the line going from (-2, 2) to (2,8). a) Find the length of this line. b) Find the midpoint of the line. c) write an equation for this line. my answers- a) 2√10 b) 0,5 c) y = 1.5x + 5 please check these answers.
31. ### Math

Determine an equation in simplified form, for the family of quadratic functions with zeros -1 -+ √5 and 2 -+ √2 B) determine an equation for the member of the family whose graph has a y intercept of -32
32. ### math

Suppose the the limit as x approaches 6 to the left equals infinity. What conclusion can be made about the graph of y = f (x)? there is a horizontal asymptote at y = -6 there is a horizontal asymptote at y = 6 there is a vertical asymptote at x = -6 there is a vertical ...
33. ### Algebra 2

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3
34. ### PreCalc

Graph y=2csc(x-π) New period that I solve for 0<x-π<2π π<x<3π What is my quarter period? I got that it was 3π/4 but when I add this to pi 4 times o reach 4π instead of 3π. Please help.
35. ### Economics

Suppose demand and supply functions are given by: 2 1 4 1 2 1  7    x s x x d x Q P and Q P a. Determine equilibrium P and Q in this market b. Use graph to show market equilibrium
36. ### math

Each time Kristine gets paid, she spends \$20 and saves the rest. If the amount Kristine earns is represented by x and the amount she saves is represented by y, which graph models her savings?
37. ### Algebra

Find a trigonometric equation in the form y = a sin (b (x-c)) which has a minimum of (3, -5) and a zero value of (6, -1). There is a graph with the minimum and the zero value labeled. It is wavy with suggests that it is a sin curve.
38. ### algebra

I have a problem with this: y=1.5x Questions: What is the rate of change between the variables? State whether the y values are increasing or decreasing, or neither, as x increases Give the y intercept List the coordinates of two points that lie on the graph of the line in the ...
39. ### algebra

graph the following function on the set of axes below. f(x) = lxl, -3 less than or equal to x less than 1 and 4, 1 less than or equal to x less than or equal to 8
40. ### Physics -work shown

A heavy conductor (mass m, length `, resistance R) is suspended by two springs each with spring constant k, and connected to a battery with electric potential V as shown in the figure. A magnetic field ~B is now imposed. The acceleration of gravity is 9.8 m/s2 . Which ...
41. ### pre-algebra

I have two questions about finding the slope of a line. First question: Is the formula Y2-Y1 over X2-X1? Second question: When I am given a line on a graph, how do I find Y1, Y2, X1, X2 to use in finding the slope?
42. ### phsics

The graph in Figure 10-22 shows the force and displacement of an object being pulled. Figure 10-22 (a) Calculate the work done to pull the object 7.0 m. 1150 J (b) Calculate the power that would be developed if the work was done in 2.4 s. Enter a number.2 W
43. ### Physics (vectors)

Please help me with this question about vectors. Thanks. If you are given a graph with a vector starting at the point (1,-1)and the arrow goes to the point (0,-4). What is the vector in rectangular coordinate? I answered (0,-3), but the coordinate for x is wrong and I can't ...
44. ### Find the function

Find the function that is finally graphed after the following transformations are applied to the graph of y=√x in the order listed. 1) Reflect about the x-axis 2) Shift up 7 units 3) Shift right 4 units
45. ### Geometry

1.) A skateboard ramp has a 158° entry angle. Find the measure of ∠1. 2.) Which of the following equations is parallel to the line passing through A(-2, 7);B(-2, -2)? 3.) Which of the following equations would graph a line parallel to 3y = 2x - x + 5? *Please help me!
46. ### Graphing Reciprocal Trig Functions

a) y=csc(x-3) I understand that there are asymptotes at 0, pi, and 2pi and I know how to graph the base points but I am confused on how to move it with the phase shift. Do I use a table of value for the asymptotes and base points to move?
47. ### Statistics

Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking—even if they are not exposed to the usual pattern of sunlight. To test ...
48. ### Algebra, Trig

Question: A wind turbine has a total height of 50m, with 3 equally spaced blades that are 16m in diameter. 1) Create equations modelling the height of points on the tips of blades One, Two and Three. Graph these three curves on one graph. [Answers: Blade 1: y=8sin(x)+42 Blade ...
49. ### physics

U(J) 6 | | 4 | \ | 2 \ ______/ \ / \_____/ 0 1 3 5 7 8 x(cm) Best I could do in drawing a graph!! A 10 g particle has the potential energy shown in the figure above. Part A: How much work does the force do as the particle moves from 2 cm to 6 cm? W = ? J Part B: What speed ...
50. ### Math

A group of students is entering a contest to win \$1000. The students plan to divide the money equally. Construct a graph that best describes the relationship between the number of students in the group and the amount of prize money each student wims?
51. ### Calculus

assume that f(x)= x^3(x-2)^2 a) find the x-intercepts algebraically b) find all the critical points c) use the first derivative test to determine local minimums and maximums d)find all inflection points e)state the concavity of the graph on appropriate intervals
52. ### calculus

given the following piecewise function x+11 for -9<=x<-3 y= { 2 for -3<=x<=2 2x-6 for 2<x<=5 a. find the domain b. find the range c. find the intercepts d. is f continuos on its domain. If not, state where f is discontinious e. graph the function This symbol...
53. ### calculus

A bug crawls along the graph of 2 y x x    4 1 , where x and y are positive and measured in centimeters. If the x-coordinate of the bug’s position x y,  changes at a constant rate of 3 cm/min, how fast is the y-coordinate changing when...
54. ### Maths

Given the equation y=2x-4 of an exponential function f 1)write down the equation of horizontal asymptote of f 2)determine the y intercept of f 3)determine the y value of a point on f with x=-2 4)draw the graph of the function of f showing all critical poins and asymptotes 5)...
55. ### pre cal

Find a possible formula for the function graphed below. Assume the function has only one x-intercept at the origin, and the point marked on the graph below is located at (2,12). The asymptotes are x=−2 and x=1. Give your formula as a reduced rational function.
56. ### Physics

A superhero flies 185 m from the top of a tall building at an angle of 15◦ below the horizontal. What is the horizontal component of the superhero’s displacement? Draw the vectors to scale on a graph to determine the answer. Answer in units of m. Your answer must be ...
57. ### Math

Given the bar graph below, create a grouped frequency distribution: Hours per week: 0 1 2 3 Mike 4 5 Don 6 Daniel 7 Jake, Greg 8 Asad 9 Sandra 10 Drake 11 12 Andrea 13 This is what i got, please tell me if i did this correctly :) Hours per week # of persons 3 1 5 1 6 1 7 2 8 1...
58. ### Math

Given the bar graph below, create a grouped frequency distribution: Hours per week: 0 1 2 3 Mike 4 5 Don 6 Daniel 7 Jake, Greg 8 Asad 9 Sandra 10 Drake 11 12 Andrea 13 This is what i got, please tell me if i did this correctly :) Hours per week # of persons 3 1 5 1 6 1 7 2 8 1...

The graph give the acceleration a versus time t for a particle moving along an x axis. The a axis scale set by a=12 m/s^2. At t = -2s the particle's velocity is 10 m/s. What is its velocity at t = 6s. I know that I am supposed to used integrals to solve, but I can't figure it ...
60. ### precalculus

How do you do this question? 1. A speed versus time graph shows the segment from (3, 4) to (8,4). The units for the vertical axis are m/s. If the object whose speed was being graphed is 8 m away from the point from which measurements are made at t= 3s, how far away is the ...
61. ### arithematic

A hat company is designing a one size fits all hat with a strap in the back that makes the hat smaller or larger. head sizes normally range from 51 to 64 centimeters. what absolute value inequality models the different sizes of the hat? graph the solution
62. ### Geometry

Myles was asked to draw a triangle xyz and then dilate it using the origin aa the center of dilation and a scale factor of 0.75.he thinks adding 0.75 units to the coordinates of the vertices of xyz will help him draw the dilated image. Explain why miles is incorrect,and what ...
63. ### Math

Consider the squaring function: The output is the input times itself. For example, if the input is 3, the output is 9. Determine which of the following points are on the graph of the squaring function: (6,36), (4,8), (-2,4), (-3,-6), (5,25), (6,12), (-6,36)
64. ### chemistry HELP plz!

What value should theoretically be obtained for the intercept on a graph of mass vs volume? HINT: The intercept corresponds to zero mass and zero volume.
65. ### Clueless in calculus

The function f is defined by f(x)= (25-x^2)^(1/2) for -5 less than or = x less than or = 5 A) find f'(x) B) write an equation for the tangent to the graph of f at x=3 C) let g be the function defined by g(x)= (f(x) for -5<or=x<or=-3)and (x+7 for -3<or=x<or=5) D) ...
66. ### Calculus

A function f(x) is continuous for all x and has a local minimum at (1,8). Which must be true? A. f'(1)=0 B. f' exists at x=1 C. The graph is concave up at x=1 D. f'(x) is less than 0 if x is less than 1, f'(x) is greater than 0 if x is greater than 1 E. f'(x) is greater than 0...
67. ### Help !

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3
68. ### Math

The function −2𝑓(2𝑥 + 4) − 1 has been transformed from the graph of 𝒇(𝒙) = 𝒙^𝟑 Write the equation for the transformed function.
69. ### Linear Equation

I posted a question below but forgot to put in the equation! So sorry. The problem states: Find 2 numbers that satisfy the equation then graph it. The equation is 2y+2=0 I think one of the numbers is -1, but what could the other be or am I doing the problem incorrectly? Thanks...
70. ### Algebra

I am not too sure about this problem. Can you please help me? Graph the ellipse and locate the foci. 9x^2=144-16y^2 I got (- squareroot 7, 0) and (squareroot 7,0), but I was looking at one problem in one book similar to it, and it had the answer as (0, - squareroot 7) and (0, ...
71. ### ALGEBRA

suppose that someone has said that the equation connecting points ((-1,1) and (2,3) is y= 2/3x + 5/3. This person wants to know whether the line represented by this will contain point (6,9). Identify two ways by which this person can decide whether the graph of the equation ...
72. ### College Math

I have been struggling with this problem I cannot get the right answer. Please give me the steps to solve this problem. Let f(x)= (2x-9)(x^2 + 6) (A) Find the equation of the line tangent to the graph of f(x) at x=3 (B) Find the values(s) of x where the tangent line is ...
73. ### math

You have \$47 to spend on music and movie downloads. Each album download costs \$7 and each movie download costs \$8. Write and graph a linear inequality that represents this situation. Let x represent the number of albums and y the number of movies.
74. ### Algebra

Use the function below to answer the following parts. 1/3x - 4 if -6 </= x < - 3 f(x) = 2 if -3 < x < 3 x^2 - 4 if x > 3 I found out the domain, range, and points of disontinuity. I think i did them right: Domain= [-6,infinity] Range= [-6,infinity] and points of...
75. ### linear programming

Minimize z = 3x + 6y subject to: 4x + y ≥ 20 x + y ≤ 20 x + y ≥ 10 x ≥ 0 y ≥ 0 Graph the feasibility region. Identify all applicable corner points of the feasibility region. Find the point(s) (x,y) that minimizes the objective function z = 3x + 6y.
76. ### math

You have \$47 to spend on music and movie downloads. Each album download costs \$7 and each movie download costs \$8. Write and graph a linear inequality that represents this situation. Let x represent the number of albums and y the number of movies.
77. ### pre-calculus

solve the equation 1. In x + In (x+12) =2 x= ? or either there is no solution 2. solve the exponential equation 9^x=6 What is the exact answer? 3. Use transformations to indentify the graph of the function. Then determine its domain, range, and horizontal asymptote. f(x)=2^-x+...
78. ### Math (algebra)

Hi could you please help me with this algebra question. A rectangle has one corner on the graph of y=36-x^2, another at the origin, a 3rd on the positive y-axis, and the fourth on the positive x-axis. Express the area A of the rectangle as a function of x. What is the domain ...
79. ### Calculous

g(x) = x^4-8x^3-16x^2+128x the graph goes through the x through (-4,0) , (0,0) (4,0), (8,0) horizontal axis has a scale of 2,4,6,8,10 (each tick increases by 2) Y-axis value that is the highest is (-4,30) and (8,30) Assume g(x) = k(x-p)(x-q)(x-r)(x-s) p<q<r<s I need ...
80. ### Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (1,1) intersect the curve again? 2. Find the constants A, B so that if Y = Asin X = B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points om he graph of Y - e^x - e...
81. ### Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he graph of Y = e^x - e...
82. ### stats

8.a) Consider the data below for Alaska Airlines and for American West Airlines. Construct a bar graph which breaks down the data by airline and by city, and which shows, for each airline, the percentage of on-time flights at each city.
83. ### Math. Pls. Help!

What factors should you consider when determining the best graph or display to represent a given set of data? In your answer, choose a set of data relevant to your life and explain the best way to display it.
84. ### Math

can someone explain this? The following is a frequency data set for test scores in a small class. Construct a cumulative frequency plot displaying data. Then describe the graph in a sentence or two. test scores: 40-49:1 50-59:2 60-69:2 70-79:7 80-89:9 90-99:5
85. ### graphing

a union charges each employee a one-time \$100 initiation fee plus \$25.00 union dues eachh month. my equation for the function is y=\$25 x + 100. how do i graph the function for the domain of 0 months to 12 months. please help
86. ### Calc AB

What is the area of the region in the first quadrant enclosed by the graph of y=e^(x^2/4) and the line y=0.5? When I graphed the two functions they don't even connect so the answer would be infinity. What am I doing wrong> Integrate y=e^(x^2/4) from x=0 to the point where e...
87. ### calculus

sorry for the probably simple question, but i haven't done this stuff in a long, long time. thought i had this right, but again not finding the answer which of the following gives the slope of the tangent line to the graph of y=2^(1-x) at x=2? a)-1/2 b)1/2 c)-2 d)2 e)-(ln2)/2 ...
88. ### Maths algebra

The efficiency of an industrial pump decreases by a fixed percentage each year. The percentage decrease each year is with respect to the efficiency of the pump at the start of each year. Over each four year period, the efficiency decreases by 80%. Let us write e = f(t) so that...
89. ### math help please im stuck!

1)Describe how you translate the graph y = ãx to y = 2 + ã(x +1). 8)Solve ã 3b = -3 10)For the triangle shown: 3 sided Kinda like --> /\ the right long side is 8 the left is 3 a.Find the missing length= b.Find the area= c.Find the perimeter= 11)Given the points: (-...
90. ### Analytical Chemistry

Given a 300 ml solution containing 0.2M H2L+ calculate the pH after the addition of 130.00 ml of 0.6M KOH. -----pH = 9.377 What total volume of KOH must be added to reach pH of 10.00 ---0.386 moles However, I am getting an amount of ml that is way too high, according to the ...
91. ### Math

y^2=8(x-3) how would you get the coordinates. vertex = 3,0 then what? let x=1, or -1, and solve for y. This is a parabola, if you are graphing, you will need several points to plot. vertex = (3,0) using x = 2 (2,4) (2,-4) > +3 translation = (5,4) (5,-4) Is this correct?? so...
92. ### Titration Graph?

Use a spreadsheet to prepare a family of graphs for the titration of 50.0 mL of 0.020 M H2A with 0.100 M NaOH. Consider the following cases: (a) pK1 = 4.00, pK2 = 8.00; (b) pK1 = 4.00, pK2 = 6.00; (c) pK1 = 4.00, pK2 = 5.00.
93. ### Pre-Algebra

Here's the instructions for my portfolio: 1. Choose two animals with different speeds. You can choose fro m the chart that starts at the bottom of this page or do research to choose your own. 2. Design a fair race in which the two animals have an equal chance of winning if ...
94. ### calculus

5). Find the volume of the solid of revolution generated by rotating the graph of y=8 lnx about the y-axis between y=0 and y=16 Answer choices: 238.39pi, 246.39pi, 230.39pi, 214.39pi, 222.39pi 7). Find the area of the region bounded by y=√x-2, y=9, y=0, x=0
95. ### infinite discontinuity

How do check the graph of a function has an infinite discontinuity at a point or not? (without the help of a graphing calculator) example: Check whether y = (x^2-9)/(3x-9) has an infinite discontinuity at x = 3 or not CAn you get rid of the denominator? (x+3)(x-3)/3(x-3) in ...

Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function Line f(x) = 2x^2 6x – y + 4 = 0 I know i have to find derivative 1st which will be f'(x)=4x but then how to i find equation do i plug 6 in for x so 4(6) would it be 6x-24???
97. ### Math

The depth d in feet of the water in a bay at is given by d(t) = 3/2 sin (5πt/31) + 23 where t is time. Graph the depth of the water as a function of time. What is the maximum depth of the water to the nearest tenth of a foot?
98. ### Calculus

consider the function y = 2sinx a) determine dy/dx b) calculate the exact value of x for which the slope of the tangent to the graph is √2 in the interval [0, pie] c) determine the equation of the tangent in part (b). d) determine the y-intercept of the tangent in part (c).