Answer
$f(x)=\frac{x^4}{12}+8x+4$
Work Step by Step
$f''(x)=x^2\hspace{8mm}f'(0)=8\hspace{8mm}f(0)=4$
$\int f''(x)dx=\int x^2dx=\frac{x^3}{3}+C=f'(x)$
$f'(0)=\frac{0}{3}+C=8$
$C=8$
$\int f'(x)dx=\frac{x^4}{12}+8x+C=f(x)$
$f(0)=\frac{0}{12}+0+C=4$
$C=4$
$f(x)=\frac{x^4}{12}+8x+4$
