Question

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

Answer 1

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'=-2x=0->x=0`

Fill in for `y`:
`y(0)=2-0^2=2`

Maximum is at `(0,2)`
graph{2-x^2 [-10, 10, -5, 5]}