Mean Value Theorem

Definition

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on an open interval (a, b), then there exists at least one point c in (a, b) where the instantaneous rate of change (derivative) equals the average rate of change over the interval.

Related terms

Secant Line:

A secant line is a straight line connecting two points on a curve. In the context of the Mean Value Theorem, it represents the average rate of change over an interval.

Concavity:

Concavity refers to whether or not a graph curves upward or downward. It plays an important role in understanding how derivatives behave and relates to the second derivative test.

Critical Point:

A critical point occurs when either the derivative of a function equals zero or does not exist. In relation to the Mean Value Theorem, critical points can help identify where instantaneous rates of change equal average rates of change.