calculas

posted by Sagar

consider the following.
Function
y = cos 3x
point (pi/4, -square root of 2/2)

(a) Find an equation of the tangent line to the graph of f at the given point. (Let x be the independent variable and y be the dependent variable.)

  1. Steve

    first, find the slope of the tangent line anywhere:

    y' = -3sin(3x)
    so, at x=π/4, y = -3sin(3π/4) = -3/√2

    Now you have a point and a slope, so the line is

    y + 1/√2 = -3/√2 (x - π/4)

Respond to this Question

First Name

Your Answer

Similar Questions

  1. calculus

    Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent …
  2. 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 …
  3. 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 …
  4. 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) …
  5. 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 …
  6. 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 …
  7. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
  8. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
  9. 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?
  10. 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)

More Similar Questions