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

Question

2019 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-05T23:35:59

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

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

$f(x)$ 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]}

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