How to Use Extreme Value Theorem

Below are the steps to use the extreme value theorem.

Step 1: Check whether the function is differentiable or not.

Step 2: If a function is differentiable, it is a continuous function.

Step 3: Then, find the first derivative of the function and equate it to 0.

Step 4: Find the critical points of the function.

Step 5: Put the critical points in the function and find its value.

Step 6: Put the points present in the specified closed interval and find the function value.

Step 7: Identify the maximum and minimum value of the function from the obtained values.

• Minimum of the function is the minimum among obtained values and the point is called the point of minimum.
• Maximum of the function is the maximum among obtained values and the point is called the point of maximum.

Article Related to Extreme Value Theorem:

• Calculus in Maths
• Differential Calculus
• Integral Calculus
• Mean Value Theorem
• Cauchy’s Mean Value Theorem

Extreme value theorem proves the existence of the maximum and minimum value of the function if the function is continuous in the closed interval [a, b]. In this article, we will discuss the extreme value theorem in depth along with the extreme value theorem statement, extreme value theorem proof and how to use the extreme value theorem. We will also solve some examples related to the extreme value theorem.

Let’s start our learning on the topic “Extreme Value Theorem.”