# Maxima And Minima

Maxima and Minima of a function together can be called as extrema. Maxima and minima can be defined as largest and smallest of a function at a given Point in its Domain or outside its domain. We can calculate the maxima and minima of a function by using maxima and minima Calculus.

To calculate maxima and minima we should follow the steps below-

1 ) Calculate f' ( x ).

2 ) Now putting f' ( x ) = 0 , we will get two values of ' x '.

3 ) We will now calculate f'' ( x ) and put first value of ' x ' in f'' ( x ).

4 ) If value of f'' ( x ) is positive than function is minimum otherwise function is maximum.

## Maximum and Minimum values of a function in its domain

The maximum and minimum values of a function collectively known as extrema .These are the smallest and largest values that a function takes at a Point in a given neighborhood local or relative extrema or on its Domain which is entirety global or absolute extrema. The Set of unbounded infinite real Numbers have no minimum and max...Read More

## Local Maxima and Local Minima

Local maxima is the Point that is at the peak with respect to the local surrounding points. Similarly, local minima can be defined as the lowest point with respect to the surrounding points. Maxima or minima can be many points as they are considered locally in the graph. It also resembles with the Set theory in a context that we have least and peak points i...Read More

## First order Derivative test for Local Maxima and Minima

Local maxima of a function can be define as a function z=f(x) is said to be attains a local maximum value at x=a if there exist a neighborhood of ‘a’ such that f(x)<f(a)for all x belongs to the (neighborhood of ‘a’) and x is not equals to ‘a’. in such a way ,f(a) is known as local maximum value of f(x) at x=a.
Now let us define lo...Read More

## Higher order derivative test

The higher order derivative in the Calculus mathematics is a technique to find the Point of inflection in the function. Generally, it is used in the calculus for the purpose of finding the maxim’s and minima's of a time differentiable and time varying Functions.

Higher order Derivatives are the type of derivatives which are found by performing several...Read More

## Point of Inflection

Inflection points can be defined as the points where a function has a change in its concavity. If second derivative of a function is positive, than it forms an upper concave, but if second derivative of a function is negative than it forms a down concave. The Point at which function changes the concave up to concave down or from concave down to concave up, at this...Read More

## Properties of Maxima and Minima

A function can take two typeof values that are classified as maxima and/or minima. The Maxima and Minima are also given a name, which is extrema. We can think of maxima and minima as the functional value which can be the highest and the lowest possibility of it. Extrema can be called as global or local. As the name directly indicates a global maximum i...Read More

## Maximum and Minimum values in a closed interval

Let g(x) is a real function defined on an interval ‘I’. Then g(x) is said to have the maximum value in the interval ‘I’ if there exist a Point ‘c’ in the interval ‘I’ such that, g(x) ≤ g(c) for all ‘x’ belongs to ‘I’.
In this case the number g(c) is called the maximum value of g(x) in the interval ‘I’ and the point ‘c’ is known as a point...Read More