Let f be continuous and differentiable on [-2, 5]. If f(-2) = 3 and f(5) = -6, then the Mean Value Theorem for derivatives guarantees that..:

Question

1. f(0) = 0
2. f'(c) = −97−79​ for at least one c between -2 and 5.
3. −6≤f(x)≤3−6≤f(x)≤3 for all x between -2 and 5.
4. f'(c) = 0 for at least one c between -6 and 3.
5. f(c) = 1 for at least one c between -2 and 5.

Answer 1

There exists -2<c<5 such that f'(c)= -9/7