# How do you determine the concavity for f(x)=x^4 ?

$f \left(x\right) = {x}^{4}$ is concave upward on $\left(- \infty , + \infty\right)$.
$f ' \left(x\right) = 4 {x}^{3}$
$f ' ' \left(x\right) = 12 {x}^{2} \ge q 0$,
which means that $f '$ is increasing on $\left(- \infty , + \infty\right)$,
which means that $f$ is concave upward on $\left(- \infty , + \infty\right)$.