on [-1.1], does the Mean Value Theorem apply? Why or why not. Find the largest a

Question

on [-1.1], does the Mean Value Theorem apply? Why or why not. Find the largest and the smallest values of the function f(x) = 4x3 -24x2 +36x + 1 on the interval [1, 5]. We do not know the equation of y = f(x) However we do know that f'(x) =4/3x1/3(x-1). What are the critical numbers (x values) for f? Find intervals where f s increasing and intervals where f is decreasing. For each of the critical numbers found in part a), determine whether the critical number gives rise a local maximum a local minimum, or neither.

Explanation / Answer

Let , a = -1and b=1. We have On the other hand, for any , not equal to 0, we have So the equation does not have a solution in c. This does not contradict the Mean Value Theorem, since f(x) is not even continuous on [-1,1]. 2)min 1 at x=3 max 17 at x=1

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