# How to find critical points and the using the first derivative test for f(x) = 3x^4 - 4x^3 + 6?

$f \left(x\right) = 3 {x}^{4} - 4 {x}^{3} + 6$
Derivative: $f ' \left(x\right) = 12 {x}^{3} - 12 {x}^{2} = 12 {x}^{2} \cdot \left(x - 1\right)$
$f ' \left(x\right) = 0$ when $x = 0$ and $x = 1$. The critical points are: $\left(0 , 6\right)$ and $\left(1 , 5\right) .$