# How do you find the inflection points for f(x)=x^4 ?

Oct 25, 2014

The following is the definition of inflection points by James Stewart.

By taking derivatives,

$f \left(x\right) = {x}^{4} R i g h t a r r o w f ' \left(x\right) = 4 {x}^{3} R i g h t a r r o w f ' ' \left(x\right) = 12 {x}^{2}$

Since $f ' ' \left(x\right) \ge 0$ for all $x$, $f$ never changes its concavity.

Hence, $f$ has no inflection point.

I hope that this was helpful.