Question

Suppose f is continuous on [a, b] and differentiable on (a, b). If f(a) = f(b), then there exists at least one number c between a and b such that $f'(c) = 0$ is the statement of

• A. Lagrange’s mean value theorem
• B. Rolle’s Theorem
• C. Fundamental theorem of calculus
• D. Fundamental theorem of algebra

Hint:

If you see the condition $f(a) = f(b)$ leading to $f'(c) = 0$, it is always Rolle's Theorem. If $f(a) \neq f(b)$ leading to a non-zero slope, it is Lagrange's Mean Value Theorem.

Answer 1

The Correct Option is B