# 1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) 2. Find an equation of the line that passes through the point (9,7) and is perpendicular

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### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the graph of f(x) = -2x3...

### calculus

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (64, 8), we know that (64, 8) is a point on the line. So we just need to find its slope. The slope of a tangent ...

### cal

find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph the quadratic function obtained and the 3 ...

### math

i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation of the line through the points at ( -9, -9) ...

### Calculus Please someone help

1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) 2. Find an equation of the line that passes through the point (9,7) and is perpendicular to the line 5x+3y-4=0

### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point. Sketch the curve and the...

### College Calculus

Let f(x) = 3x^2 - 2x + 1 a) write an equation of the line going through the points (1, f(1)), and (2, f(2)). b) Find a point on the graph of f where the tangent line to the graph has the same slope as the line in part (a). Write the equation of the tangent line at that point. ...

### Calc.

Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, and shade the area under the tangent. Find out...

### Math Please Help!!

Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x)=-10/3x^2+6x+6; (-1, -10/3) slope ?? tangent line y = ?

### math

Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x)=-10/3x^2+6x+6; (-1, -10/3) slope ?? tangent line y = ?

### Calculus

Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x) = -8/5 x^2 + 7 x + 7;(-1, -8/5) slope tangent line y =

### Math

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 9/(5 x) ( at ) \(1,(9/5)) m = y=

### math

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=7x-5x^2 at (-2,-34) m = ?? y = ?? .

### Calculus

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/4 x at (1,15/4)

### Calculus

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/(4 x) at (1,(15/4) m = y =

### Calculus

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 7 x - 2 x^2 text( at ) \(-1,-9\) m = y =

### Calculus PLEASE HELP

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 2 x - 4 x^2( at ) (-2,-20) m= y=

### calculus

Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)

### Calculus

Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = -2x2-2x+1 (-1, -2)

### Calculus

55. Find an equation of the tangent line to the graph of f(x) =x^3 - 2x + 1 a) at (2,5); b) at (-1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x) - (3/2) b) No solution c) No solution For each function, find the points on the graph at which the tangent line is ...

### Math (equation of tangent line)

Consider the implicit equation 2xy-1=(x+y+1)^2 a) Compute and solve for the derivative dy/dx as a function of x and y. b) Find the equation of the tangent line to the graph of the above when y=-1. For part a, I found the derivative being equal -(x+1)/(y+1) but how would I find...

### Applied Calculus......

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=6x-5x^2 at (-2, -32) I have to use the four step process, but seem to be getting stuck...

### Algebra

graph the equation x-3=y (where do I plot the points?) find the intercepts and then graph: 5x+4y=20 find the intercepts and then graph: 1.4x-1.3y=3.64 graph the equation using slope and y-intercept: y=10/7x +4 graph using slope and y-intercept: x+2y=8 graph by plotting points ...

### Calculus

1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) passes through the point (0, -8) which is not...

### Calculus

The equation dy/dx = -6x^2/y gives the slope at any point on the graph of f(x). The range of f(x) is [0, infinity] and f(1) = 2. A. Find the equation of the tangent line to f(x) at the point (1,2). B. Write the function f(x). C. Determine the domain of the function f(x).

### Math--Calculus

Let y = f(x) be the continuous function that satisfies the equation x^4 - (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2. (a) Find and expression for y'. (b) Write an equation for the line L. (c...

### calculus

5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the secant line on the interval [1, 3].

### Math (Calculus) (mean value theorem emergency)

Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in the interval (-2,4) such that the tangent ...

### calculus

find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8

### Algebra

Is it possible to find the slope of a line if the equation has two ys? Find slope of the line whose equation is 8y = 7 - 2y Solve for y and you'll have a horizontal line. Combine the y terms. 8y+2y=7 10y=7 y=7/10 The general equation for a straight line is y = mx + b m is the ...

### Calculus

How do you find the original function given a point (a,b) and the equation of the line tangent to the graph of f(x) at (a,b). For example: The point is (4,-11) and 7x-3y=61 is the equation of the line tangent to the graph of f(x)

### Calculus

1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the definition f’(x) = lim(h→0) Determine the...

### Calculus

1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the definition f’(x) = lim(h→0) Determine the...

### Calculus

1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) f(x)=9x -2x +6

### Calculus A

1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) f(x)=9x -2x +6

### Math (Calculus 121)

The derivative tells you the slope at any point. df/dx = 8 x^3 - 12 x When x = 3, the slope is m = 8*27 - 36 = 180 and the equation of the tangent line is (y - 228) = 180*(x - 3) y = 180 x - 540 + 228 = 180 x - 312 wow, that was absolutely correct (i just plugged it into ...

### math

Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. f(x)=x^2/x+4 ; (3,9/7)

### math

Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. F(X)=x^2/x+6;(3,1) m = ?? y = ??

### math

Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. f(x)=x^2/x+4 ;(1,1/5) m =?? y =??

### math

Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. f(x)=x^2/x+4 ;(1,1/5) m =?? y =??

### Calculus AB

Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of x^2 - 3xy + y^2 = 1 ...

### Calculus

1) An equation of the line contains points (7/9, 7) and (-7/9) is 2) Find the slope of the line tangent to the curve y=x^2 at the point (-0.6, 0.36) and find the corresponding equation of the tangent line

### Calculus derivative

find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the derivative equation?

### calculus

I'm feeling pretty stupid right now because I can't remember how to do these. if f(x) = (2x-5)/(x^2-4), write an equation of the tangent line to f at point x=0. *How do I find the slope of the tangent line? and how do you put x=ln4 into a y= equation? Take the derivative of f(...

### calculus

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. 10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x) 11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has a slope of 0. 12. If the slope of a ...

### calculus

This is from our problem set. f(x)= 2(x^3)-3(x^2)-12x+20 write an equation of the line perpendicular to the graph of f at x=0 I think i'm supposed to take the derivate of f and then find the slope of the tangent line at x=0. Then take the opposite reciporcal of that and put ...

### Calculus

The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals of (0.12,1), if any, is the graph of g ...

### Math- calculus

Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an equation of the line tangent to the graph of f at x = -1 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0,-8) which is not of the graph of f. Find a and b...

### Math please help

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???

### MATH

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???

### Calculas

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???

### calculus totally confused

find a first degree polynomial function p(1) whose value and slope agree with the value and slope of f at x=c. i think you use taylor series for this f(x)=4/sqrt(x), c=1 i'm totally confused on how to do it. i know you find the derivative but how do i get the function. this is...

### Calculus: for mathmate

Find the slope of the tangent line to the graph of the given function at any point: 1. f(x)= 13 I understand that you said the tangent to the line is the coefficient of x, but what would be the slope of this problem. For problems like this are there specific steps to take?

### Physics

can someone help i'm stuck on two questions??? 23. On a velocity-time graph, when is the object not moving? when the slope is a straight line rising to the right when the slope is a straight line falling to the right when the slope is a line curving upward to the right at the ...

### Calculus

find an equation of the tangent line to the graph of the function f through the point (xsub0, ysub0) not on the graph. TO find the point of tangency (x,y) on the graph of f, solve the equation ....

### Calculus

Find the equation of the tangent to the graph of f(x)=2x^4 (to the power of 4) that has slope 1. Derivative is 8 x^3. This equals 1 at x = 1/2. At this point the y-coordinate is f(1/2) = 1/8. The equation of the tangent line is thus: 1/8 + 1*(x-1/2) = x - 3/8 Thank you for ...

### Math

Suppose f(x)=5/(x-2). f'(5)=-5/9. Use this to find the equation of the tangent line to the curve y=5/x-2 at the point (5,(5/3)). write your answer in the form y=mx+b where m is the slope and b is the y-intercept. The equation of the tangent line is.....

### Calculus

Let f(x)=3x^4-2x^2+3 a) find f'(x) Answer: f'(x)=12x^3-4x b) find the slope of the line tangent to the graph of f at x=3. Answer:312 So I got those firs two right but what I need help with is part C which is c) find an equation of the line tangent to the graph of f at x=3

### algebra

1. Given the line with the equation : a) Find at least three ordered pairs that satisfy the equation. b) Find the slope of the line. c) Graph the line 2. Given the line with equation : a) Write the equation in slope-intercept form. b) State the slope of the line. c) State the ...

### College Math

2008 (2nd)Course2-4.1 We are to find a function f(x) such that its derivative is x^2+x-1 and the graph of y=f(x) is tangent to the straight line y=x+1. First we find the coordinates of the point at which y=f(x) and y=x+1 are tangent.Since the slope of the tangent line is A,the...

### Calc

Write the equation of the line tangent to the graph of the function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. (1/x^3 -x)^2 at x= 2

### Math please.

What is the y-intercept of y = 2/3x + 2? I have to write it out but how? A line has a slope of 1/2 and passes through the point (0,5). What is the equation of the line? A)y = 1/2x + 5 B)y = 1/2x - 5<--- C)y = 5x + 1/2 D)y = -5x + 1/2 Find an equation of the line that passes...

### Calculus

Find an equation for the tangent line of the function y=x+(4/x) at the point (2, 4). The equation of the tangent line is . You may enter the equation in any form.

### calculus

1. Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (-2, -2). Let l be the line tangent to the graph of f at x = 2. a. Find an expression for y’ b. Write an equation for line l

### calculus

1. Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (-2, -2). Let l be the line tangent to the graph of f at x = 2. a. Find an expression for y’ b. Write an equation for line l

### Math

I have a series of questions that I did. They lead up to the last question I can't solve. Could you check my math and help me with the last question? Thanks! a) Let a be the point (2,3). Compute the distance from Origin 0 to A answer: a^2 + b^2 = c^2 3^2 + 2^2 = c^2 c=sqrt(13...

### I would like to understand my calc homework:/

Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the point (1,1). Then use your tangent line equation...

### Calculus

Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the following equation of f '(x). f '(x) = y0 − y/x0 − x f(x) = √x (x0, y0) = (-16, ...

### calc

Find an equation of the tangent line to the curve at the given point. y = 6 x sin x P= (pi/2 , 3pi) i know the slope of a tangent line is equal to the first derivative. For that I got 6xcosx + 6sinx but idk how to put that into the y-y1=m(x-x1) formula to make the equation

### Calculus

Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on the graph of f where the line tangent to the...

### Calculus

Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on the graph of f where the line tangent to the...

### Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a and b #2. Let h be a function defined for all...

### math

Find the equation of the tangent line to the graph of f(x) = 2x − 6/x + 1 at the point at which x = 0. (Let x be the independent variable and y be the dependent variable.) I got this question wrong. I thought the answer would be y=-4x-6 I followed the following steps: 1...

### calculus

find an equation for the line with the given properties. express the equation in slope-intercept form. containing the pointsP=(-1,1)& Q= (1,-2) What is the equation of the line? y= Find the the equation of a line that is perpendicular to the line y=1/2x+4 and contains the ...

### calculus

for the function f(x)=4x^2 +7, find the equation of the tangent line to the graph of f at x+1. if the equation of the tangent line is written as y=mx+b. m=? b=?

### Math

What is the solution of the following equation? 2 – 8x = -6 Is the ordered pair (-2, 9) a solution of the equation y = x - 7? Solve the following equation. 3(z – 2) – z = 4z – 20 Find the slope of the line that passes through the points (4, 8) and (10, 5) using the ...

### Calculus

Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point. (x - y - 1)3 = x; (1, -1)

### Calculus

Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point. (x - y - 1)3 = x; (1, -1) y =

### Math

What is the y-intercept of y = 2/3x + 2? I have to write it out but how? A line has a slope of 1/2 and passes through the point (0,5). What is the equation of the line? A)y = 1/2x + 5 B)y = 1/2x - 5<--- C)y = 5x + 1/2 D)y = -5x + 1/2 Find an equation of the line that passes...

### Calculus

I am unsure of how to take the derivative of this equation. It may be the exponents that are giving me trouble but I'm not sure exactly. Find the equation of the tangent line to the curve 4e^xy = 2x + y at point (0,4). On the left side, is the "xy" the exponent of e, or do you...

### Geometry

How do I write an equation of a line perpendicular to the graph of -2y + x =-5 that passes through the point at (1,2) Given the line -2y + x =-5, solve for y so the equation is in this form: y = mx + b Once you know the slope, m, you also know the slope of the perpendicular ...

### Calculus

Find the slope and equation of the tangent line to the graph of the function at the given value of x. f(x)=x^4-20x^2+64;x=-1

### Calculus

How do you find Altitude and slope slope is the derivative of a function: for ex. if you have f(x)=x^2 + x, at point (1,2) f'(x)=2x+1 your slope is 2(1) + 1 = 3 =m to find the equation is y-y1=m(x-x1) so you have: y-2=3(x-1) gives you: 3x-1 is your equation for a tangent line ...

### Math (Slope of inverse tangent line)

Given the graph, goo.gl/photos/VTMjKvNsVvAQwe3X6 a) What is the slope of the tangent line to the graph of f^-1 at the point (-1/2,-1)? b) What is the slope of the tangent line to the graph of f^-1 at the point (1,2)?

### Algebra 116

I have like 13 questions i need help with so here they go. 1. In 1991 the life expectancy of males in a certain country was 70.1 years. In 1995 it was 72.6 years. Let E representn the life expectancy in years and t represent the number of years since 1991. a.The linear ...

### CALCULUS HELP

Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. Y=(x-2)/(15-x^2) x=-4 HOW DO WE DO THIS

### calculous

3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the zeros of f b.Write an equation of the line perpendicular to the graph of f at x = 0 c. Find the x and y coordinates of all points on the graph of f where the line tangent to the graph is parallel to the x axis.

### Calculus

Find the slope of the functions graph at a given point. Then find an equation for the line tangent to the graph there. f(x)=2*square root of x. (1,2) Could someone please help me figure this one out?

### MATH

Find an equation of the line that is tangent to the graph of f and parallel to the given line. Function f(x) = 2x^2 Line 6x – y + 4 = 0

### calculus

Find an equation of the line that is tangent to the graph f and parallel to the given line Function: f(x)= 1/ square root of x Line: x+2y-6=0

### calculus

for f(x)=5/8, a. find an equation for the secant line through points where x=4 and x=5.b. find an equation for the line tangent to the curve when x=4. I can solve part a., but I am confused on part b. please help. I don't understand how to plug the numbers into the equation f(...

### Calculus 2nd Post please help

Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point. (x - y - 1)3 = x; (1, -1)

### Math- Calculus

Find an equation of the line that is tangent to the graph of f and parallel to the given line Function: f(x) = x^3 Line 3x-y+1 = 0 ._.; I know the derivative of the function is 3x^2 and I do have the answer in the back of my book just need the way to get it..

### AP Calculus

Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0. A. Does f have an inflection point at x=0? Explain your answer. B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g. Write the equation of...

### Calculus

I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). Therefore the slope of the tangent line at x=...

### calculus 1

The point P(2,-1) lies on the curve y=1/(1-x) If Q is the point (x, 1/(1-x) find slope of secant line. these are the points 2, -1 1.5,2 1.9,1.111111 1.99,1.010101 1.999,001001 2.5,0.666667 2.1,0.909091 2.01,0.990099 2.001,0.999001 using the results from the points guess the ...

### calculus

i'm not sure how to do this. can someone help, please? thanks! consider the function f(x0 = x^2 + 2x on the interval [-2, 2] a. draw a sketch of the graph of f(x). find the average rate of change on the interval [-2, 2] and sketch this secant line. b. find an expression that ...

### My Daughter Stacy needs help in math plz help!

You have to find the x and y coordinates:(She doesn't get it and neither do I) 2x + y = 9 The question doesn't go with the equation. I suspect it is a plotting exercise Make a table x y Put in for x 0, 1, 4 Solve for each corresponding y. Then graph the points, and connect ...

### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the graph of f(x) = -2x3...