Consider f ' (x) = 6x^2 + 2 and (-1,2) lies on the graph of f. Find the equation for f(x).

Answer 1

f ' (x) = 6x^2 + 2

We first take the antiderivative of f'(x).

f(x)=2x^3+2x+c

Next we solve for c by putting in (-1,2) in the function f(x)

2=2(-1)^3+2(-1)+c

2=-4+c

6=c

Replace c with 6 in our function f(x) and we are done.

f(x)=2x^3+2x+6