# What are the local extrema, if any, of f(x)= x^2-1?

Dec 3, 2015

$\left(0 , - 1\right)$

#### Explanation:

Local extrema occur when $f ' \left(x\right) = 0$. So, find $f ' \left(x\right)$ and set it equal to $0$.

$f ' \left(x\right) = 2 x$

$2 x = 0$

$x = 0$

There is a local extremum at $\left(0 , - 1\right)$.

Check a graph:

graph{x^2-1 [-10, 10, -5, 5]}