calculus

posted by .

Consider the function.
f (x) = 5x3 + 3x
(a) Compute the derivative at x = 3 using the limit definition.
f '(3) =
(b) Find an equation of the tangent line.
2

  • calculus -

    evaluate f(3)
    evaluate (3+h) and simplify

    then take
    Limit [ (f(3+h) - f(3) ]/h as h --->0

    You should be able to factor out an h from the top which would then cancel the h in the bottom
    you should get
    f'(3) = 138

    b) when x=3, y = 138 (that's a coincidence)
    so you have
    slope of tangent is 138 and (3,138) is a point on it

    y = 138x + b , plug in the point
    138 = 138(3) + b
    b = -276

    so y = 138x - 276 is the tangent equation

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. ap calculus ab

    for f(x)=lnx we know that f(e)=1. Use the tangent line at(e,1) to compute the tangent line approximation of f(3). what does the difference between the actual value and the tangent line approximation have to do with the concavity (2nd …
  3. 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 …
  4. 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 …
  5. 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)
  6. Calculus

    If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x …
  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

    Using the definition of the derivative, find the equation of the tangent line to y=2x-1/2 at (1/2,-1) Thanks!!
  9. 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 …
  10. 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 …

More Similar Questions