$f(x)=\sqrt[\phantom{2}]{5x^3+12x^2}$

Use graphing technology $($e$.$g$.,$ Desmos $[)$ to help answer the following question$($s$).$ Round your answer$($s$)$ to three decimal places.

a$.$ The function has a local maximum of $y=$ at $x=$

b$.$ The function has a local minimum of $y=$ at $x=$

c$.$ The function is increasing on the interval$($s$)$

d$.$ The function is decreasing on the interval$($s$)$

$$

e$.$ The domain of the function is

f$.$ The range of the function is