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

$f(x)=x^3-27x+2$

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

$$

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

$$

$($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.

$(x,y)=$

Find the interval where the graph is concave upward. $($Enter your answer using interval notation.$)$

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Find the interval where the graph is concave downward. $($Enter your answer using interval notation.$)$

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$($d$)$ Use the information from parts $($a$)-($c$)$ to sketch the graph. Check your work with a graphing device if you have one.