What are the critical points of f(x) = -3x^4 + 12x^3 + 6?

Jul 4, 2016

$x = 0$ an inflexion

$x = 3$ a max

Explanation:

$f \left(x\right) = - 3 {x}^{4} + 12 {x}^{3} + 6$

$f ' \left(x\right) = - 12 {x}^{3} + 36 {x}^{2} = 12 {x}^{2} \left(3 - x\right)$

$f ' ' \left(x\right) = - 36 {x}^{2} + 72 x = 36 x \left(2 - x\right)$

$f ' = 0 \setminus \implies x = 0 , 3$

$f ' ' \left(0\right) = 0$ ie an inflexion

$f ' ' \left(3\right) = - 108$ ie a max