Question

What are the absolute extrema of `f(x)= 2 + x^2 in [-2, 3]`?

Answer 1

`f(x)` has an absolute minimum of 2 at `x=0`

Explanation:

`f(x)= 2+x^2`

`f(x)` is a parabola with a single absolute minimum where `f'(x)=0`

`f'(x) =0+2x = 0 -> x=0`

`:.f_min(x) = f(0) = 2`

This can be seen on the graph of `f(x)` below:

graph{2+x^2 [-9.19, 8.59, -0.97, 7.926]}