Taylor is studying the function $f(x)=x^3-2.$ They want to prove that $f(x)$ takes on a minimum value over the interval $-3,2.$

Determine whether Extreme Value Theorem applies or not; if it applies, find the minimum value that is guaranteed by the theorem.

EVT applies: minimum value is $-29.$

EVT applies: minimum value is $-3.$

EVT does not apply.

EVT applies: minimum value is $2.$

EVT applies: minimum value is $6.$