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.

Solve Examples with Mean Value Theorem

mvt problem 1 →mvt problem 2 →

More Calculus Topics

Product Rule
The product rule for finding the derivative of two functions multiplied together.
L'Hôpital's Rule
Using derivatives to find limits of indeterminate forms.
Implicit Differentiation
How to differentiate equations where y is not explicitly isolated.