Discussion
Cauchy's mean value theorem differs from Lagrange's in that it
Answer: B
Cauchy's form states that \( [f(b)-f(a)]/[g(b)-g(a)] = f'(c)/g'(c) \) for some interior \( c \), so two functions are compared at once. Taking \( g(x) = x \) recovers Lagrange's theorem. No second derivative is needed, monotonicity is not required, and the vanishing derivative is Rolle's conclusion
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