Consider the following function.

$f(x)=2x^3-21x^2+72x-7$

Find the derivative.

$f^{\text{'}}(x)=$

Find any critical numbers $of$ the function. $(Enter$ your answer $as$ a comma$-$separated list. $If$ any answer does not exist, enter DNE$)$

$x=$

Find the interval$(s)on$ which $fis$ increasing. $(Enter$ your answer using interval notation.$)$

Find the interval$(s)on$ which $fis$ decreasing. $(Enter$ your answer using interval notation.$)$

Find the local minimum and maximum value $off.$

local minimum value

local maximum value