Rolle's theorem requires that on [a, b], in addition to continuity + d…

Question

Rolle's theorem requires that on [a, b], in addition to continuity + differentiability:

Accepted Answer

D. f(a) = f(b) (function takes same value at endpoints)

**Rolle's theorem:** f continuous on [a,b], differentiable on (a,b), AND f(a) = f(b).
**Conclusion:** there exists c in (a,b) with f'(c) = 0. Mean Value Theorem is similar but doesn't require f(a) = f(b).

Answer

f'(a) = f'(b) (equal derivatives at ends)

Answer

f''(a) = 0 = f''(b) (zero second derivative)

Answer

f(a) + f(b) = 0 (sum is zero)

Rolle's theorem requires that on [a, b], in addition to continuity + differentiability:

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