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 $f$.