# Thread: Derivatives

1. ## Derivatives

Find f: f''=20x^3 + 12x^2 + 4 f(0)=8 f(1)=5

2. Originally Posted by jkeatin
Find f: f''=20x^3 + 12x^2 + 4 f(0)=8 f(1)=5
$f''(x)=20x^3 + 12x^2 + 4$

$f'(x)=5x^4 + 4x^3 + 4x + C_1$

$f(x)=x^5 + x^4 + 2x^2 + C_1x + C_2$

now, substitute $x=0$ and $x=1$ and you will have 2 equations and two unknowns.
and then solve for $C_1$ and $C_2$.