Let

Question

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=?

Answer 1

If you mean f(x) = (x-3)^-2,

then f is discontinuous at x=3 and the mean value theorem does not apply.