How does the Mean Value Theorem connect the derivative of a function to its average rate of change over an interval?
Answer 1
Natasha Wong
The Mean Value Theorem states that for a continuous function f(x) that is differentiable on the interval (a, b), there exists at least one point c in (a, b) where the instantaneous rate of change (the derivative f'(c)) equals the average rate of change over [a, b], i.e., f'(c) = (f(b) – f(a)) / (b – a).
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