Question

How to find critical numbers in calculus.

A) Set the derivative equal to zero
B) Identify points of inflection
C) Find the absolute maximum
D) Use the Mean Value Theorem

Answer 1

To find critical numbers in calculus, you can follow steps such as setting the derivative equal to zero and using the Mean Value Theorem.

Step-by-step explanation:

In calculus, to find critical numbers, you can follow these steps:

1. Set the derivative of the function equal to zero to find where the function's slope is zero or undefined.
2. Identify points of inflection where the second derivative changes sign.
3. Find the absolute maximum or minimum by evaluating the function at the critical numbers and endpoints of the interval.
4. Use the Mean Value Theorem to find critical points where the average rate of change is equal to the instantaneous rate of change.