# How do you find the relative extrema for f(x)=x^4 ?

Mar 30, 2018

$x = 0$

#### Explanation:

To find the extrema of a function, just evaluate its derivative and see where it equals zero.

In this case, we have

$\frac{d}{\mathrm{dx}} {x}^{4} = 4 {x}^{3}$

using the rule

$\frac{d}{\mathrm{dx}} {x}^{n} = n {x}^{n - 1}$

So, we need $4 {x}^{3} = 0 \setminus \iff {x}^{3} = 0 \setminus \iff x = 0$