Use $y=\frac{x^3(x-5{)}^2}{27}$ and its derivative $\frac{dy}{dx}=\frac{5x^2(x-3)(x-5)}{27}$ to find each of the following.

Find the critical values. $($Enter your answers as a comma$-$separated list.$)$

$x=$

Goodivork.

Find the critical points.

$(x,y)=(,)(smallestx-$value$)$

$(x,y)=(,)(largestx-$value$)$

Find the intervals on which the function is increasing. $($Enter your answer using interval notation.$)$

Find the intervals on which the function is decreasing. $($Enter your answer using interval notation.$)$

Find the relative maxima, relative minima, and horizontal points of inflection. $($If an answer does not exist, enter DNE.$)$ relative maxima

$(x,y)=(,)$

relative minima

$(x,y)=(,)$

horizontal points of inflection $(x,y)=(,)$