Consider the following. $($If an answer does not exist, enter DNE.$)$

$f(x)=x^3-6x^2+3$

$($a$)$ Find the interval$($s$)$ of increase. $($Enter your answer using interval notation.$)$

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Find the interval$($s$)$ of decrease. $($Enter your answer using interval notation.$)$

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$($b$)$ Find the local minimum value$($s$).($Enter your answers as a comma$-$separated list.$)$

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Find the local maximum value$($s$).($Enter your answers as a comma$-$separated list.$)$

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$($c$)$ Find the inflection point.

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$(x,y)=$

Find the interval$($s$)$ where the function is concave up$.($Enter your answer using interv