Which of the following statements is/are true?

If f '(x) 0 on (a, b), then f(x) is increasing on [a, b].
If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
If f(x) is differentiable at x = c, then f(x) is continuous at x = c.

Question

Which of the following statements is/are true?

If f '(x) > 0 on (a, b), then f(x) is increasing on [a, b].
If f(a) = f(b), then there exists a number c in (a, b) such that f '(x) = 0.
If f(x) is differentiable at x = c, then f(x) is continuous at x = c.

anonymous · Answer

A. I only 
B. II only
C. I and III
D. I and II

anonymous · Answer

@ganeshie8 @imqwerty

anonymous · Answer

@jigglypuff314 @Michele_Laino

ganeshie8 · Answer

for sure, III is true as differentiability implies continuity

anonymous · Answer

So maybe A. Because as f'x is greater than 0 it's increasing? @ganeshie8

anonymous · Answer

The answer is I and III