11. Consider the function f(x) = x2 on the interval [0, 1/2 ]. According to the

Question

11. Consider the function f(x) = x2 on the interval [0, 1/2 ]. According to the Mean Value Theorem, there must be a number c in (0, 1/2 ) such that f '(c) is equal to a particular value d. What is d? a. 3/2 b. 1 c. 1/2 d. 2 e. None of the above (12). Suppose f is a continuous function defined on a closed interval [a, b]. What theorem guarantees the existence of an absolute maximum value and an absolute minimum value? a. Absolute Value Theorem b. Extreme Value Theorem c. Mean Value Theorem d. Intermediate Value Theorem e. None of the abov

Explanation / Answer

a)

f'(c) = [f(b) -f(a)]/(b-a)

=> d = f'(c) = [(1/4) - 0]/(1/2) = 1/2

b)

the extreme value theorm

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