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Find the equation of the tangent line to the curve at the point .

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calculus
The function f is defined by f(x) = x^3 - x^2 - 4x + 4 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 on the graph of f. Find the values of a and b. I have no clue how to solve this I know the ...

calc
The function f is defined by f(x) = x^3 - x^2 - 4x + 4 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 on the graph of f. Find the values of a and b. I have no clue how to solve this I know the ...

calculus help
Find the points where the tangent line is horizontal or vertical. Find the area under one period of the curve. x= r(deta - cos deta) Y= r(1- sin deta)

Derivative Calculus
I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4 - 8/9x^9/8 + x^2 - 9x + 1 Answer: f’(x)= 15/4x^1/4 - x ^1/8 + 2x -9 2) Let f(x)= 7x^3 - 9x. Find f’(5) Answer: f’(x)=21x^2-9 f’(5)=516 3) Find the given limit by evaluating the derivative. lim h⇒...

Calculus
Find all points on the curve x^2y^2+2xy=3 where the slope of the tangent is -1. If there is more than one point, use a comma to separate each pair of coordinates

Maths (Tangents and Normals)
curve y = (x^2) - 4x + 5 is tangent perpendiculat to the (line = 2y + x - 7 = 0)

Calculus I
For what values of a and b is the line -4x+y=b tangent to the curve y=ax^3 when x=4? Can anyone give me the hint?

Algebra HELP!!
Write the equation of a line which contains the point (2,4) and (-2,2) y = -2x + 2 y = 2x + 4 y = ½x + 3 y = -4x + 2 The slopes has to be (2-4)/(-2-2)=-2/-4 But that's not one of the answers so what do i DO? -2/-4 = 1/2 There is no line with a slope of 1/2?? Try a point in ...

Calculus: Implicit
so i suppose to find slope. i have trouble this problem. my math book is not really clear. Find the slope of the tangent line to the curve √(3x+2y)+√(4xy)=11.6 at the point (6,2). √(3x+2y) is the square root(3x+2y) √(4xy)is the square root 4xy.

math
Find the slope m of the tangent to the curve y = 5/ sqrt (x) at the point where x = a > 0. what is the slope?

calculus
Find an equation of the line tangent to 2x^2-x-ln(x-4)-y^2=9 at (5,6)

calculus
find the equation of the tangent line to y=4^((x^2)-6x+3) at x=4

cal
find the equation for the tangent line g(x)=x-1/2x+4 at x=-1

Writing this equation
how do I write the equation of a line perpendicular to the line 6x – 3y=10 and containing the point (-6, 2). The line you are given can have its equation rewritten im y = mx + b as: y = 2x - 10/3 That tells you that is slope is m = 2. A line that is perpendicular to that ...

Calculus
I think I have the correct answers for the following problems. For anyone who has the time I would appreciate it if you could tell me if I am correct/incorrect. Thank you. 1). Differentiate ã(x)sin x = (2xcosx+sinx)/2ã(x) 2). Differentiate 2t/(4+t^2) = (8-2t^2)/(4+t^2)^2...

english
equation 4x = 5y + 7. You want to find a line that has that point and is parallel to that line. You must first convert that equation into the y = mx + b form. 5y = 4x - 7; y = 4x/5 - 7/5; we know that a parallel line has a slope that is the same which would be 4/5. Do you know...

calculus
I have two questions please. 1. find an equation for the line with the given properties. Express in slope-inntercept form. 2. find the equation of a line that is perpendicular to the line y=1/2x+4 and contains the point (-3,0) please show work

calculus
I have two questions please. 1. find an equation for the line with the given properties. Express in slope-inntercept form. 2. find the equation of a line that is perpendicular to the line y=1/2x+4 and contains the point (-3,0) please show work

AP CALCULUS
What is an equation of the line tangent to the graph of f(x)=x2(2x+1)3 at the point where x=-1? (that's x squared (2x+1)cubed) I'm having trouble finding the derivative:f'(x)which would be the slope (m).

precalculus
Find (a) the equation of a line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Write both answers in slope-intercept form. (c) Graph both of these lines on the ...

college math
find the slope of the tangent line to the graph of f at the given point. Graph f and the tangen line. 9. f(x) = 3x +5 at (1.8) 10. f(x)=2x + 1 at (-1,3) Please, help me with this problems. thanks

Calculus
Find the slope of the tangent line to the ellipse (x^2)/4 + (y^2)/9 = 1 at the point (x,y)

Calculus
If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).

Calculus
If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).

CALC
Find the tangent line to the ellipse defined by 3x^2 + 5y^2 = 17 at the point (-2, 1).

calculus
find the slope of the tangent line at the point P(1,1) on the graph of e^x-y=2x^2-y^2

math
find tangent line to the circle x^2 + y^2=100 at point (-6,8)

calculus
find the slope of the tangent line at the point (1,2) for the ellipse 2x^2+3y^2=14 y'(1) = ??

Calculus grade 12
find the slope of the tangent line to y^4 = 3x^2 - 2x at the point (1,1)

calc
Find the slope of the tangent line to the graph y = x-3 at the point (0.5, 8)

Calculus
Find the slope of the tangent line to the ellipse x^2/4 + y^2/16= 1 at the point (x,y)

equation of a line
How to find a point on the line? x cordinate is given as x. The diagram is like a rectangle is inscribed in an isosceles right triangle whose hypotneus is 2 units long. AB is another side of the right triangle and P is a point on it(also a vertex of the rectangle). How do I ...

calculus
Find a function f such that the curve y = f(x) satisfies y'' = 12x, passes through the point (0,1), and has a horizontal tangent there. I can use the anti-derivatives to get y = 2x^3 + Cx + D but I don't know how to get C even though I know D = 1.

calculus
Show that the curve given below has no tangent line with slope m1, where: y = 4 x^3 + 8 x - 6 m1 = 7

math
Determine the points on the curve y=x^2(x^3-x)^2 where the tangent line is horizontal. Thx!

cal
determine any values of x for which a tangent line to the curve f(x)=1/x will have a slope of -4

Calculus
If the line 3x-4y=0 is tangent in the first quadrant to the curve y=x^3+k, then k is? I got 1/4 is this correct?

AlGEBRA 2 (check answers plz)
What is the equation of the line that has a slope of -2 and a y-intercept of -7? y = -2x - 7 <-- y = -7x - 2 y = -2x + 7 y = -7x + 2 or <-- Find the equation of the line that has a slope of 4 and contains the point (-4, 1). y = 4x + 1 <-- y = 4x - 8 y = 4x - 15 y = 4x...

Advanced Math
1. The distance s(t) between an object and its starting point is given by the anti derivitive of the velocity function v(t). find the distance between the object and its starting point after 15 sec if v(t)=0.2t^2+2t+10 meters/seconds. MY ANSWER: 600 meters. 2.Find the slope of...

calculus
Find the equation of the tangent line to the graph of f(x)=4x^3-1x^2+1 at x=-2.

Calculus Please Help
Let f(x) = x^3 - x^2 + x - 1. Find an equation for tangent line to f at x = 2.

Calculus Please Help
Let f(x) = x^3 - x^2 + x - 1. Find an equation for tangent line to f at x = 2.

Calculus
find f(3) and f'(3), assuming that the tangent line to y=f(x) at a=3 has the equation y=5x+2.

Calculus
find an equation for the line tangent to y=2-6x^2 at (-5,-148)

math
Find f(3) and f'(3), assuming that the tangent line to y=f(x) at a=3 has the equation y=5x+2

calculus
Find an equation of the tangent line to the graph y=(x^3 + 2)^5 at x= -1

Math
Find an equation of the tangent line to the graph of y = f(x) at x = a, a = 1. f(x) = x + 3/x^2 + 1

calculus
find the equation of the line tangent to the graph y=3e^x at x=1

calculus
find the equation of the line tangent to the graph y=3e^x at x=1

Calculus 1
Given f(x)= 3e^(1-x^2)*ln(x), find the equation of the tangent line at x = 1.

Calculus
If f(1)=4 and f'(1)=2, find an equation of the tangent line at x=1 A. y=2x+2 B. y=2x-2 C. y=4x-7 D. y=4x-2 E. None of these

Calculus
Find the equation of the tangent line when x=2 for the functin f(x)=5^(x/2)

geomery
Triangle ABC, inscribed in a circle, has AB = 15 and BC = 25. A tangent to the circle is drawn at B, and a line through A parallel to this tangent intersects line BC at D. Find DC.

calculus
Help! I have a test tommorow! I don't understand (b), (c), (e), and (g). The answers are listed following the each question. Here's a discription of the graph: There is a graph of a function f consists of a semi circle (-3 to 1 faced downward on the x-axis) and two line ...

Maths
what is the equation for the tangent to the curve 6y=7-x^3 at (1,1)?

calculus
For the function y = 9x2 + 6x + 2, at the point x = 7, find the following. (a) the slope of the tangent to the curve (b) the instantaneous rate of change of the function

Chemistry
For chemistry, I have to make a line graph. My teacher specifically instructed us to make one with smooth, fluid lines, not with choppy ones, so it would form a curve. I am suppposed to find the slope of the line, but I don't know how to, because the line goes up and down and ...

Geometry
Hi, For one part of my problem I have had to find the equation of a straight line that passes through two points, I have done this but now i need to determine whether a new point lies on this line by using the equation from the first part, how would I do this please. The ...

algebra review!
it says write the equation of the vertical line that passes through the point (7,-3). what do i need to start it off? find the equation for the line with undefined slope and passing through the point (-1,-2). what do i need to start that off? what equation do i use to find the...

calculus
the curve with equation 2(x^2+y^2)^2=9(x^2-y^2) is called a lemniscate. find the points on the lemniscate where the tangent is horizontal.

Calculus
Find the slope of the tangent line to the graph of f at any given point f(x) = -2x + 6 at (2,2)

calculus
find the point(s) on the graph of y = (2x4 + 1)(x - 5) where the tangent line slope is 1.

calculus
given f(x)=ã(x). find the distance of the point P(2,5) from the line tangent to the functions at x=4.

math
Find the values of a,b, and c if the parabola y=a(x^2)+bx+c is tangent to the line y=-2x+3 at (2,-1) and has a critical point when x=3

calculus
Find the slope of the tangent line to the graph y = x-3 at the point (0.5, 8). Answer -48 -12 4 16

math class
Find the slope of the tangent line to the graph y = x^-3 at the point (0.5, 8). -48 -12 4 16

Calculus
1. If the tangent line to y=f(x) at (4,3) passed through the point (0,2), find f(4) and f'(4). My answer: f(4)=3 f'(4)=1/4

Calculus
Find a function of the form f(x)=a+bsqrtx that is tangent to the line 2y-3x=5 at the point (1, 4)

Calculus
Can anybody help me with this? Consider the surface xyz = 20. A. Find the unit normal vector to the surface at the point (1, 4, 5) with positive first coordinate. (___,___,___) B. Find the equation of the tangent plane to the surface at the given point. Express your answer in ...

calculus help please
Find the points where the tangent line is horizontal or vertical. Find the area under one period of the curve. x= r(deta - cos deta) Y= r(1- sin deta) deta= pie/3

Math/Physics
For a velocity-time graph, what does the "tangent line of the curve" represent?

AP Calculus
Find an equation of all tangent lines for the curve x^2-xy+y^2=16 x=-2 2x-(xy'+y(1))+2yy'=0 2x-xy'+y+2yy'=0 y'(-x+2y)=-2x-y y'=-2x-y/-x+2y y'=-2(0)-y/-(0)+2y y'=-y/2y Not sure what to do now?

GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION
segment BC is tangent to circle A at B and to circle D at C. (Not drawn to scale) AB=10 BC=25 and DC=3. Find AD to the nearest tenth. Hint: Draw an auxiliary line from D to segment BA. {There are two circles, the larger one has point A in the center and a dotted line going up ...

Calculus
The expression dy/dx = x*(cube root y) gives the slope at any point of the graph of the function f(x) where f(2) = 8. A. Write the equation of the tangent line to f(x) and any point (2,8). B. Write an expression for f(x) in terms of x. C. What is the domain of f(x)? D. What is...

Calculus
The City Electric System(CES) recently constructed a major transmission line along parts of South Street in the city. The transmission lines are strung between power poles and the hanging lines form a catenary curve. For this Problem we will use the following equation y=(T/w)...

calculus
find,if any, an equation for a common tangent line to these 2 curves:5x^2;and 5x^2-x+6

calculus
y=3⋅2^x Find the equation of the line tangent to the graph of y at x=1.5.

Calculus
Find the equation of the tangent line to the graph of f(x) = −6x ln(x + 10) at x = 0.

Calculus
Find the equation of the line tangent to the graph of f at (1,1) where f is given by f(x)=2x^3-2x^2+1

Ap Calculus
Find the equation of the tangent line to the graph of f(x)=cos3xlnx^4 at (1,0)

algebra 2
how to find equation of horizontal tangent line of 2y^3+6x^2y-12x^2+6y=1

Calculus
Find the equation of a circle with center C(1,6) and tangent line x-y-1=0.

Calculus
Find the equation of the tangent line to the graph of √(xy)=x-2y at (4,1)

Calculus
Find the slope of the tangent line to the graph of the equation: y = (2x^2+3)(x-1) at x=2. a = 11 b = 08 c = 19 d = 16

calculus
Find the equation of the tangent line to the graph of the function f(x)=x-3/3x-5 at x=1

maths
Find the equation of the tangent to circle x² + y² - 6x + 4y - 12 = 0 which is parallel to line 4x +3y +5

calculus
Find the equation of the tangent line to the ellipse x 2 + 4y 2 = 25 when x = 3 and y < 0. Answer 3x - 8y = 7 3x - 8y = 25 3x + 8y = 7 3x + 8y = 25

Urgent Calculus Help 2
Find the equation of the tangent line to the graph of f(x) = 6x ln(x + 4) at x = 2.

Calculus
Find the equation of the tangent line to f(x)=sec x - 2 cos x at (pi/3, 1).

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.

Linear Approximation
Use linear approximation, i.e. the tangent line, to approximate 1/0.104 as follows: Let f(x)=1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.104 . Then use this to approximate 1/0.104 . L(x)=f(a)+f'(a)(x-a)...i think. You're notation is slightly ...

Math
Find the function f, given that the slope of the tangent line at any point (x,f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=6(2x-7)^5 at (4, 3/2)

algebra
Write the equation of the line that passes through point (5, 4) with a slope of 0. would this be x=5 then? no x=5 is the equation of the vertical line passing through (5,4) Any horizontal line, (slope=0), has an equation of the form y = b notice that this is a variation of the...

Calculus
I am not sure what to do here: Find the derivative (f '(x) using the limit process a). f(x)= 2x^2+5x+2 find f ' (2) b.) Find the equation of the Tangent Line at (1,5)

Calculus
Find the linear approximation of the function f(x)=^3sqrt(1+3x) at a=0 and use it to approximate ^3sqrt(1.03)Is this an overestimate or underestimate of the actual value? Explain your answer in terms of the tangent line and the curve.

Pre- Algebra
Given an equation of a line, how do I find equations for lines parallel to it going through specified points Simplifying the equations into slope-intercept form. 1. y= -2x -4; (1, 3) how do I write the equation of a line parallel to the given line but passing through the given...

mathematics
The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2.1.1 equation of new circle which is the rotation of original circle through 180 degree around the origin...2.1.2 find equation of another circle which is the translation (x;y)-(x-8;y-6) of the points of the ...

maths
1) Circle centre (7,-2) passes through (-2,10). Calculate radius and find equation of circle. 2) AB is diameter of circle A(9,5) B(-1,-7). Find equation of circle mid point. I know i have to use the eqn (x1+x2)/2 and (y1+y2)/2 3) Find the equation of circle with centre (-8,5...

Calculus
Mathematica Project - Position, Velocity, and Acceleration? A rocket is fired vertically upward into the air from a launching platform 100 ft above the ground. The platform is then retracted, and the rocket is allowed to fall to the ground. The height (in ft) of the rocket ...

economics
elow kindy ans. my question pls.. what is optium point in budget line and indefference curve, and also what is the diff. between budget line and indefference curve?..

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