Does the function satisfy the hypotheses of the Mean Value Theorem on the given

Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? Give reasons for your answer. f(x) X819,1-2,4] Choose the correct answer below. 0 A. Yes, f(x) is continuous for every point of (-2,4) and differentiable for every point in [-2.41 O B. Yes, f(x) is continuous for every point of [ -2,4] and differentiable for every point in (-2,4) O c. No, f(x) is differentiable for every point in (-2,4) but is not continuous for every point of [-2,4] O D. No, f(x) is continuous for every point of I-2.4] but is not differentiable for every point in (-2,4)

Explanation / Answer

For Mean Value theorem to be applicable on f(x) in interval [a,b]

f(x) should be continuous on the interval [a,b] and differentiable on (a,b),

Here f(x) = x8/9 is continous everywhere in interval [-2,4] but its not differentiable for every point in (-2,4) since it is not differentiable at x = 0 which lies between -2 to 4.Thus,mean value theorem will not be applicable.

Answer is D. No, f(x) is continous for every point of [-2,4] but is not differentiable for every point in (-2,4).

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