Question

xplain WHY Rolle's Theorem can or cannot be used to state that f '(x) must be equal to 0 somewhere within the interval bounded by the zeros of this function. Next, if Rolle's does apply, find the critical number and explain how it fulfills the promise made by Rolle's Theorem.

Answer 1

Answer:

see below

Step-by-step explanation:

1. Rolle's Theorem can be used to state that f'(x) must be equal to 0 somewhere within the interval bounded by the zeros of a function. Rolle's theorem states that if f(a) = f(b) on the interval {a,b}, then there must be at least one point c within the interval {a,b} that f'(c) = 0. Since the zeros of the function have the same output 0 = 0, Rolle's theorem is applicable.

2. I can't find the critical number without the function being defined so...

but find where the derivative of f(x) is 0 on the interval {a,b} to find the critical point. if there are multiple solutions where f'(x) = 0, remember that the solution must be in the interval.