Analyze the concavity of the function and identify the inflection points.
$h\left(x\right)=-2x^4+8x^3-10x^2$

Concave up on $(1-\frac{\sqrt{6}}{6},1+\frac{\sqrt{6}}{6})$

Concave down on $(-\infty ,1-\frac{\sqrt{6}}{6})\cup (1+\frac{\sqrt{6}}{6},\infty )$

Inflection points at $x=1-\frac{\sqrt{6}}{6},1+\frac{\sqrt{6}}{6}$

Concave up on $(-\infty ,1-\frac{\sqrt{6}}{6})\cup (1+\frac{\sqrt{6}}{6},\infty )$

Concave down on $(1-\frac{\sqrt{6}}{6},1+\frac{\sqrt{6}}{6})$

Inflection points at $x=1-\frac{\sqrt{6}}{6},1+\frac{\sqrt{6}}{6}$

Concave up on $(-\infty ,1-\frac{\sqrt{6}}{6})$

Concave down on $(1+\frac{\sqrt{6}}{6},\infty )$

Inflection points at $x=1+\frac{\sqrt{6}}{6}$

Concave up on $(1+\frac{\sqrt{6}}{6},\infty )$

Concave down on $(-\infty ,1-\frac{\sqrt{6}}{6})$

Inflection points at $x=1-\frac{\sqrt{6}}{6}$