How to Find Points of Maxima and Minima? (First Derivative Test)
In any smoothly changing function, the points where the function flattens out, give us either minima or maxima. Now, this statement gives rise to two questions.
- How to recognize the points at which function flattens out?
- Suppose we got a point at which function flattens i.eofcritical point. How to tell whether it’s a minimum or a maximum?
To answer the first question let’s look at the slope of the function. The points where the function flattens out have zero slopes. We know that the derivative is nothing but the slope of the function at a particular point. So, we try to find the points where the derivative is zero. Thus, this test is also called the First Derivative Test. Then we equate the differential equation with zero to get the critical points as,
f'(x) = 0
The solution to this equation gives us the position of the critical points. These critical points tells us that these are the points where the tangent to the curve is parallel to x-axis but still we don’t know whether they are points o maxima or minima for that Second Derivative test is used.
Relative Minima and Maxima
Relative maxima and minima are the points defined in any function such that at these points the value of the function is either maximum or minimum in their neighborhood. Relative maxima and minima depend on their neighborhood point and are calculated accordingly. We find the relative maxima and minima of any function by using the first derivative test and the second derivative test.
In this article, we have covered Relative Maxima and Minima, methods to find relative maxima and minima, various examples, and others in detail. Before starting with Relative Maxima and Minima, first, learn in brief about Maxima and Minima.
Table of Content
- What is Maxima and Minima?
- What Is Relative Maxima and Minima?
- How to Find Points of Maxima and Minima?
- Recognizing Maxima and Minima
- Steps to Find Relative Maxima and Minima