How to Perform First Derivative Test?

To Perform the First Derivative Test, we can use the following steps:

Step 1: Find f'(x) for the function f(x).

Step 2: Put f'(x) = 0 and solve this equation and obtain different values of x say a, b, c….

Step 3: To test the point x = a, determine the sign of f'(x) for values of slightly less than and slightly greater than a, and see which of the following condition holds true:

• If f'(x) changes sign from positive to negative, then x = a is the point of the local maximum, and f (a) is a local maximum value.
• If f'(x) changes sign from negative to positive, then x = a is the points of the local minimum, and f (a) is a local minimum value.
• If f'(x) does not change its sign, then x = a is a point of inflexion.

Step 4: Similarly, repeat the test for the points x = b, x = c, etc.

Let’s consider the following examples for better understanding.

First Derivative Test is the test in calculus to find whether a function has a maximum or minimum value in the given interval. As the name suggests, the first derivative is used in this test to find the critical point and then further conditions are used to check each critical point for extrema. Many times in our daily life, we come across many situations where we wish to find the maximum and minimum of something, in those cases, we can use the First Derivative Test if we can mathematically define that situation.

In this article, we will learn this important test i.e., “First Derivative Test”, other than this we will also learn how to use this test to find the extrema of the function as well as solved examples of the same. So, let’s start learning about one of the fundamental tests in calculus i.e., the First Derivative Test.