analyze-if-the-piecewise-function-hxx32x3x23x24x12-and-ltx1hleftxrightbegincases

Question

Analyze if the piecewise function $h (x) = {\begin{matrix} x^{3} - 2 x, - 3 \leq x \leq - 2 \\ 3 x^{2} - 4 x + 1, - 2 < x \leq - 1 \end{matrix}$ satisfies the Mean Value Theorem criteria over the domain of the function.

Accepted Answer

The function does not satisfy the hypotheses of the Mean Value Theorem.

Answer

The function satisfies the hypotheses of the Mean Value Theorem.

Analyze if the piecewise function h(x)={x3−2x,−3≤x≤−23x2−4x+1,−2<x≤−1h\left(x\right)=\begin{cases}x^3-2x,-3\le x\le-2\\ 3x^2-4x+1,-2<x\le-1\end{cases} satisfies the Mean Value Theorem criteria over the domain of the function.

Analyze if the piecewise function $h (x) = {\begin{matrix} x^{3} - 2 x, - 3 \leq x \leq - 2 \\ 3 x^{2} - 4 x + 1, - 2 < x \leq - 1 \end{matrix}$ satisfies the Mean Value Theorem criteria over the domain of the function.