$2.($Extreme Value Theorem$)*$

Solve the following problem.

Which of the following statements is true?

$($a$)$ A continuous function defined on a bounded interval that excludes one of its endpoints attains both a maximum and a minimum.

$($b$)$ A function that is differentiable on a closed interval attains a maximum and minimum on that interval.

$($c$)$ The Extreme Value Theorem applies to functions that are continuous on intervals of the form $\backslash ([$a$,\backslash$infty$)\backslash ),$ as long as the function itself is bounded above on that interval.

$($d$)$ A continuous real$-$valued function defined on a compact subset of $\backslash (\backslash$mathbb$\{$R$\}\backslash )$ attains both its maximum and minimum values.

$($e$)$ The Extreme Value Theorem ensures that the maximum and minimum values of a function occur at interior points of the domain.

$($a$)$

$($b$)$

$($c$)$

$($d$)$

$($e$)$