Mathematica(@mathemetica):The Mean Value Theorem If 𝑓 is continuous on [𝑎, 𝑏] and differentiable on (𝑎, 𝑏), then there exists some 𝑐 with 𝑎 < 𝑐 < 𝑏 such that 𝑓′(𝑐) = [𝑓(𝑏) − 𝑓(𝑎)] / (𝑏 − 𝑎) This means the instantaneous rate of change at 𝑐 equals the average rate of change of 𝑓 over [𝑎, 𝑏].

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Mathematica@mathemetica

2026.05.17 07:38

The Mean Value Theorem If 𝑓 is continuous on [𝑎, 𝑏] and differentiable on (𝑎, 𝑏), then there exists some 𝑐 with 𝑎 < 𝑐 < 𝑏 such that 𝑓′(𝑐) = [𝑓(𝑏) − 𝑓(𝑎)] / (𝑏 − 𝑎) This means the instantaneous rate of change at 𝑐 equals the average rate of change of 𝑓 over [𝑎, 𝑏].