Question

If a function f(x )is continuous in [2,5] , differentiable in (2,5) and f(2) = f(5) then how many value x can have where f'(x) nullifies for sure?

• A. zero
• B. More than one
• C. At most one
• D. At least one

Answer 1

The correct option is D

At least one

If we recall the definition of rolle’s theorem, it states that if we have a function which is continuous in [a,b] , differentiable in (a, b) and f(a) = f(b), then there is at least one c , between a to b such that f’(c) = 0. We get the same conditions in the given question. So the definition states that there could be more than one values of x where the derivative nullifies. But at least one value of ‘x’ will be there.