Locate the critical points of $h\left(x\right)=x^3-6x^2+9x$, and use the Second Derivative Test to identify whether these points are local maxima, minima, or neither.

Consider the function $f\left(x\right)=x^3{e}^{-2x}$. Its critical points are located at $(0,0)$ and $(\frac{3}{2},\frac{27}{8e^3})$. Use the Second Derivative Test to identify whether these points are local maxima, minima, or neither.

Find the extreme values of $f\left(x\right)=\frac{242}{5}{x}^5-\frac{3874}{3}{x}^3+32x$. Round to two decimal places if necessary.

Find the inflection points of the function $y=\frac{2x^5}{5}-5x^3+6$. Determine the intervals of concavity as well.

Determine the inflection points and intervals of concavity for the function $f\left(x\right)=3\sin x+2x^2$, $-2\pi \le x\le \pi$.