Question

How to find where instantaneous rate of change is equal to average rate of change?

A) Evaluate the derivative.

B) Use the mean value theorem.

C) Apply L'Hôpital's rule.

D) Solve a system of equations.

Answer 1

The mean value theorem is used to find where the instantaneous rate of change is equal to the average rate of change.

Step-by-step explanation:

The method to find where the instantaneous rate of change is equal to average rate of change is B) Use the mean value theorem.

The mean value theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in the open interval (a, b) such that the derivative of the function at c is equal to the average rate of change of the function over the interval [a, b].

By applying the mean value theorem, we can find the point where the instantaneous rate of change is equal to the average rate of change.