The slope f '(x) at each point (x, y) on a curve. y = f (x) is given along with a particular point (a, b) on the curve. Use this information to find f (x). [CLO-3] f '(x) = 9 x 2 + 4 x - 4; (0, -7)

Step-by-step explanation:

Integrating each term with respect to x, we get:

            x^3          x^2

f(x) = 9 + 4 - 4x + C

               3            2

We are told that if x = 0, f(x) = -7, and so C must equal - 7.  

The solution is

            x^3          x^2

f(x) = 9 + 4 - 4x - 7,   or   f(x) = 3x^3 + 2x^2 - 4x - 7

               3            2