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Asked • 07/04/20

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

2 Answers By Expert Tutors

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Shin C. answered • 07/04/20

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UCLA Undergrad Expert/Enthusiast in Calculus, K-12, and SAT Math

Stephanie B. answered • 07/04/20

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5 (4)

High School/College Algebra and Trig, Statistics, and Chemistry

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