Question

Which of the following condition satisfy for Mean Value Theorem?
1. f (a) = f (b)
2. \(\rm\frac{[f (b) - f(a)] }{(b - a)}\)
3. \(\rm\frac{[f (b) - f(a)] }{[g (b) - g (a)]}\)
4. f (a) = f (b) = f' (c)

Answer 1

Correct Answer - Option 2 : \(\rm\frac{[f (b) - f(a)] }{(b - a)}\)

Explanation:

(Mean Value Theorem) Let f  : [a, b] → R be a continuous function on [a, b] and differentiable on (a, b). Then there exists some c in (a, b) such that

 f'(c) = \(\rm\frac{[f (b) - f(a)] }{(b - a)}\)