Calculus

Can someone show how to solve this problem

Find the equation of the tangent line to the curve given by,

x=3e^t
y=5e^-t

at the point where t=0

Thanks!

  1. 👍
  2. 👎
  3. 👁
  1. one way:

    when t = 0
    x = 3
    y = 5

    dy/dx = dy/dt * dt/dx

    dy/dt = -5 e^-t

    dx/dt = 3 e^t
    so
    dt/dx = (1/3) e^-t

    dy/dx = -5 e-t (1/3)e^-t
    dy/dx = -(5/3) e^-2t = -5/3 when t = 0
    so
    y = -5/3 x + b
    5 = -5/3 * 3 + b
    b = 10
    so
    y = -5 x/3 + 10

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line

  2. AP AB Calculus

    Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the

  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

  4. calculus

    Use implicit differentiation to find an equation of the tangent line to the curve. sin(x+y)=4x−4y at the point (π,π). Tangent Line Equation:

  1. math

    how do i solve this problem? find an equation for a line that is tangent to the graph of y=e^x and goes through the origin.

  2. 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

  3. calculus

    Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the

  4. calculus

    -find the equation of the tangent line to the curve y=5xcosx at the point (pi,-5pi) -the equation of this tangent line can be written in the form y=mx+b where m= and b= -what is the answer to m and b?

  1. 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 = ?? .

  2. Calculus 1

    Find the equation of the tangent line to the curve y=6xcosx at the point (pi,-6pi) The equation of this tangent line can be written in the form y=mx+b What is m ? What is b ?

  3. Calculus

    1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at

  4. math

    Use implicit differentiation to find the equation of the tangent line to the curve xy3+xy=14 at the point (7,1) . The equation of this tangent line can be written in the form y=mx+b i don't seem to no how to find m or b

You can view more similar questions or ask a new question.