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The geometric meaning is that each small horizontal step uses its own local slope. The resulting vertical increments accumulate to the total rise from $f(a)$ to $f(b)$.

Conditions: Viewing the theorem through the lens of Riemann sums or local linear approximation.; The function is differentiable on the interval.

The geometric meaning is that each small horizontal step uses its own local slope. The resulting vertical increments accumulate to the total rise from $f(a)$ to $f(b)$.

Conditions: Viewing the theorem through the lens of Riemann sums or local linear approximation.; The function is differentiable on the interval.