Question

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....Select one:

a. f(c) = 0
b. f '(c) = 0
c. f (c) = 5
d. f '(c) = 5

Answer 1

The answer would be B, because in order for the function to have two values of x where the function value is the same, it must have a point in the function where it is a max or min. Because it has a max or min, at that point, the slope of the function is 0, meaning that B is the correct answer because B states that at that point that is a max or min, the slope of the function is 0.