A chemical is poured into cylindrical and conical flasks at a constant rate. It takes $8$ seconds to fill each flask to the brim. If $d\left(t\right)$ represents the depth of the chemical at any time $t$ in $0\le t\le 8$, for which flask does $d^{\prime }$ reach an absolute maximum on the interval $[0,8]$?

Find the absolute maximum and minimum values of the function $h$ on the interval $[-1, 3]$.

$h(x) = 5x^3 e^{-2x}$

Find the critical points, the absolute maximum value, and the absolute minimum value of the function $h\left(x\right)=3^x\sin x$ on the interval $[-1,4]$ (round to three decimal places). Also, plot the function using a graphing utility.