AP CALCULUS

posted by .

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).

  • AP CALCULUS -

    To find the derivative, you must use the product rule
    f'(x) = u'*v + u*v'

    So,
    f(x) = x^2*(2x+1)^3
    f'(x)=(2x)(2x+1)^3+(x^2)(3)(2x+1)^2(2)
    (need chain rule, too)

    Simplify
    (2x)(2x+1)^2(5x+1)
    (10x^2+2x)(2x+1)^2

    In the form
    y-y1 = m(x-x1)
    y+1 = (10x^2+2x)(2x+1)^2(x+1)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. 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: …
  3. 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 …
  4. Calculus

    An equation of the line tangent to the graph of y=(2x+3)/(3x-2) at the point (1,5) is...do I take the derivative of y=(2x+3)/(3x-2) to find the slope and then plug that into y-5=m(x-1)?
  5. 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). …
  6. calc

    What is an equation of the line tangent to the graph of f(x)=x2(2x+1)3 at the point where x=-1?
  7. 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 …
  8. calculus

    If (x) =3x squared - x cubed, find f prime(1) and use it to find an equation of the tangent line to the curve y=3(x) squared - x cubed at a point (1,2)
  9. 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?
  10. calculus

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

More Similar Questions