 # Mean Value Theorem

Let f(x) = (x − 3)−2.

Find all values of c in (25) such that f(5) − f(2) = f'(c)(5 − 2).

 This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (2, 5) such that f '(c) = f(5) − f(2) 5 − 2

.

 This does not contradict the Mean Value Theorem since f is not continuous at x = 3.    This does not contradict the Mean Value Theorem since f is continuous on (2, 5), and there exists a c on (2, 5) such that f '(c) = f(5) − f(2) 5 − 2

.

 This contradicts the Mean Value Theorem since there exists a c on (2, 5) such that f '(c) = f(5) − f(2) 5 − 2

, Lois C.

For the Mean Value theorem to apply, the function must be continuous on the given interval, but at x = 3, the function has a discontinuity. The apparent choices of possible answers don't seem to cite this as a reason why the MVT doesn't work.
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07/04/20

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