# Given the function y=2-x^2, how do you determine the relative maximum or the relative minimum?

Aug 6, 2015

You set the derivative to zero. If the sign before the ${x}^{2}$ is a minus (which it is), we search for a maximum (a "mountain" parabola)

#### Explanation:

$y ' = - 2 x = 0 \to x = 0$

Fill in for $y$:
$y \left(0\right) = 2 - {0}^{2} = 2$

Maximum is at $\left(0 , 2\right)$
graph{2-x^2 [-10, 10, -5, 5]}