# How do you find the local max and min for f(x) = 1 - sqrt(x)?

Dec 15, 2016

Local maximum is $1$ (at $x = 0$).

#### Explanation:

$f ' \left(x\right) = - \frac{1}{2 \sqrt{x}}$

$f ' \left(x\right)$ is never $0$ and is undefined at $x = 0$ which is int he domain of $f$. So $0$ is a critical number.

$f '$ is not defined left of $0$ and is negative $r i g h t o f$0$, s o$f(0) = 1# is a local maximum.

There are no other critical numbers, so there are no other local extrema.