Determine whether the Mean Value theorem can be applied to f on the closed inter

Question

Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 4 x , [21, 4] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = f(b) f(a) b a . (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot be applied, enter NA.) c =

Explanation / Answer

f(x) =4- x is a polynomial function but it is not continuous in the closed interval (-21,4).

f(4) =4-4 =0 (so function is not continuous at x=4.

Hence , as per mean value theorem if a function is not continuous then there does not exist c value in the interval.

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