Question

How do you find the critical numbers for `f(x)= x^2 - 4` to determine the maximum and minimum?

Answer 1

There is one critical point at `(0,-4)` and it is a minimum.

Explanation:

`f(x)=x^2-4`
`f(2)=2^2-4=0`
`:. f'(x)=2x`

At a max/min `f'(x)=0=>2x=0 => x=0`

And, `:. f''(x)=2=> f''(2) > 0 =>`minimum
graph{x^2-4 [-10, 10, -5, 5]}