If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 < c < 2 such that (4 points)

Question

If f(x) = ι(x2 - 8)ι, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the mean value theorem? (

Answer 1

study any proof of the MVT or Rolle's Theorem for the first one.

For the 2nd one, since f satisfies the conditions of the MVT, and is concave down over the whole interval, there is but one number c in the interval.