Question

Find and classify all critical points of function.
ok so if there is only 1 critical point and say it is a minimum. It would be an absolute minimum right?

Answer 1

yes, unless the end points of the interval are lower.

Answer 2

for f(x) defined on -infty<x<infty
then in the interval of x=ALL REAL NUMBERS f'(c) denotes an absolute minimum for f(x), however if the interval is limited to x in [a,b]
we need to check f(a) and f(b) as well as f(c) and see which is smallest.