Mean Value TheoremMediumQuestion 310008
Question
Rolle's theorem requires f(a) = f(b) and:
- Af continuous on [a,b] and differentiable on (a,b)Correct
- Bf is constant
- Cf is linear
- Df'(a) = f'(b)
Correct answer
f continuous on [a,b] and differentiable on (a,b)
Explanation
Rolle's theorem: if f is continuous on [a,b], differentiable on (a,b), and f(a) = f(b), then ∃ c ∈ (a,b) such that f'(c) = 0.