Theorems
Mean Value Theorem
A fundamental theorem linking the average rate of change to the instantaneous rate of change.
The Mean Value Theorem (MVT) states that if a function f is continuous on [a, b] and differentiable on (a, b), there exists at least one point c in (a, b) such that f'(c) = [f(b) - f(a)] / (b - a). This theorem provides deep insights into the behavior of derivatives.