If f(x) is differentiable for the closed interval [−4, 0] such that f(−4) = 5 and f(0) = 9, then there exists a value c, −4

Question

If f(x) is differentiable for the closed interval [−4, 0] such that f(−4) = 5 and f(0) = 9, then there exists a value c, −4 < c < 0 such that

A. f(c) = 0
 B. f '(c) = 0
C.  f (c) = 1
D. f '(c) = 1

anonymous · Answer

f'(c) = slope between the endpoints

anonymous · Answer

thank you!!!!

anonymous · Answer

so its f'(c) = 1?

jim_thompson5910 · Answer

You probably already figured it out by now, but you are using the Mean Value Theorem for this problem http://mathworld.wolfram.com/Mean-ValueTheorem.html

jim_thompson5910 · Answer

yes the slope between the two points is 1, so f ' (c) =1 for some value of c in the interval [-4,0]