Question

If f(x) is differentiable for the closed interval [−1, 4] such that f(−1) = −3 and f(4) = 12, then there exists a value c, −1< c < 4 such that

f '(c) = 3
f '(c) = 0 '
f(c) = −15
f (c) = 3

Answer 1

Intermediate value theorem states that if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.

So there should be a value between -3 and 12, which would be f(c)=3

Answer 2

f(c) = 3 is not the correct answer