APFIVE Mean Value Theorem Application
Let $$f$$ be the function defined by $$f(x) = \displaystyle \frac{1}{4}x^4 - \frac{2}{3}x^3 + \frac{1}{2}x^2 - \frac{1}{2}x$$. For how many values of $$x$$ in the open interval $$(0, 1.565)$$ is the instantaneous rate of change of $$f$$ equal to the average rate of change of $$f$$ on the closed interval $$[0, 1.565]$$?
A
Three
B
Four
C
Zero
D
One
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