Question
Find the value or values of $c$ that satisfy Equation (1) in the conclusion of the Mean Value Theorem for the functions and intervals.$$f(x)=x^{3}-x^{2}, \quad[-1,2]$$
Step 1
This is given by the formula: $$\frac{f(b)-f(a)}{b-a}$$ where $a$ and $b$ are the endpoints of the interval. In this case, $a=-1$ and $b=2$. So we have: $$\frac{f(2)-f(-1)}{2-(-1)}=\frac{(2^3-2^2)-((-1)^3-(-1)^2)}{2-(-1)}=\frac{8-4-(-1-1)}{3}=\frac{2}{3}$$ Show more…
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