Discussion
None of these four is the geometric reading of Lagrange's mean value theorem except
Answer: A
The theorem says \( f'(c) = [f(b)-f(a)]/(b-a) \): a tangent somewhere inside has the same slope as the chord, so the two are parallel. A horizontal tangent is Rolle's special case, and neither an interior crossing nor a curve staying above its chord follows, the latter being a statement about convexity instead
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