# Thread: Absolute max and min

1. ## Absolute max and min

Find the absolute max and min values of the function, if they exist, over the indicated interval.

F(x) = x (square root of x+3) ; [-3,6]

2. Originally Posted by littlesohi
Find the absolute max and min values of the function, if they exist, over the indicated interval.

F(x) = x (square root of x+3) ; [-3,6]
$f(x)=x\sqrt{x+3}$

$f'(x)=\frac{x}{2\sqrt{x+3}}+\sqrt{x+3}$

$=\frac{3x+6}{2\sqrt{x+3}}$

The critical numbers are given by

$3x+6=0$

$x=-2$

So $f(-2)$ should be an extreme point.

So to determine whether it's a max or min you can just examine points write around $f(-2)$ and see if they are less than or great than $f(-2)$.