Analyze the concavity of the function and identify the inflection points.

$h\left(x\right)=-2x^4+8x^3-10x^2$

Determine the intervals on which the function $g\left(x\right)=2x^6-18x^5+45x^4+50$ is concave up or concave down. Identify any inflection points.

The figure shows the graph of $f^{\prime }$ on the closed interval $[-6,3]$. Locate the inflection point(s) of $f$.

The graphs of the first and second derivatives of $f$ are shown. Which of the following graphs is the possible graph of $f$?

Consider the graph of a twice-differentiable function $f\left(x\right)$. Determine whether $f^{\prime }\left(x\right)$ and $f^{\prime }$${}^{\prime }\left(x\right)$ are positive, negative, or zero at point $A$.