Mean VAlue Theorem

Question

Let f(x) = (x − 3)⁻².

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

 (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

c = 

 

Based off of this information, what conclusions can be made about the Mean Value Theorem?

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

,

 but f is not continuous at x = 3.Nothing can be concluded.

Answer 1

The function f(x) = (x-3)^-2 = 1 / (x-3)² is not continuous at x = 3. So, the MVT does not apply on the given interval