Extrema Calculator

Introduction to Extrema Calculator:

Local Extrema Calculator is an online tool that helps you find a given function's extrema point in a few seconds. Our tool evaluates the relative maxima or relative minima values of a function on a graph of a curve line.

It is an amazing source that provides solutions for complex or lengthy calculations of a given function in one click only. You just need to give the input value in this saddle point calculator and it will generate a function solution without taking any external assistance.

What is an Extreme Point?

An extrema function is a procedure that is used in calculus to find the extrema points and critical points of a given function. It refers to different conditions for specific functions to determine the critical points.

This process helps to identify the points where a given function reaches its local maximum or minimum values. These extrema points are crucial for solving calculus, engineering, and scientific problems easily.

How to Calculate Absolute Extrema Point?

The extreme points calculator uses the differentiate method to calculate the absolute extrema point. After the derivation of a given function, it uses certain conditions that define the local maxim or minim points of the given function at particular points.

Here is the complete calculation process of the extreme values calculator to let you know the whole process of finding absolute extrema.

Step 1:

Identify the given function f(x) and differentiate it with respect to x

Step 2:

To find the critical point, the extreme calculator usually takes the result of the first derivative function equal to zero as f′(x)=0 or uses the algebraic method to get a solution in a and b values.

Step 3:

Then again differentiate the result of the first derivative with respect to x

Step 4:

Apply the condition of the extrema point to find the local maxima or minima value.
$$ f′′(x) > 0\; (local\; minimum) $$

$$ f′′(x) < 0\; (local\; maximum) $$

$$ f′′(x) \;=\; 0\; then\; the\; test\; fail $$

Step 5:

Put the critical point value in the given function f(x) one by one

Step 6:

Lastly, use the local maxima or minimum point and sketch a graph to get a visual understanding of the given function.

Practical Example of Extrema Point:

An example of an extrema point is given below to let you know how the relative extrema calculator works and solves the problems.

Example:

$$ f(x) \;=\; x^3 - 3x^2 + 2x $$

Solution:

Given function is,

$$ f(x) \;=\; x^3 - 3x^2 + 2x $$

Differentiate with respect to x,

$$ f’(x) \;=\; \frac{d}{dx}(x^3 - 3x^2 + 2x) $$

$$ f’(x) \;=\; 3x^2 - 6x + 2 $$

Solve the result of derivation by keeping it equal to zero for the critical point,

$$ 3x^2 - 6x + 2 \;=\; 0 $$

This is a quadratic equation so used its formula to get a solution,

Here, a = 3, b = -6 and c = 2.

$$ x \;=\; \frac{-(-6) \pm \sqrt{(-6)^2 - 4 . 3 . 2}}{2 . 3} $$

$$ x \;=\; \frac{6 \pm \sqrt{36 - 24}}{6} $$

$$ x \;=\; \frac{6 \pm \sqrt{12}}{6} $$

$$ x \;=\; \frac{6 \pm 2\sqrt{3}}{6} $$

$$ x \;=\; 1 \pm \frac{\sqrt{3}}{3} $$

So the critical point is,

$$ x_1 \;=\; 1 + \frac{\sqrt{3}}{3} $$
$$ x_2 \;=\; 1 - \frac{\sqrt{3}}{3} $$

Differentiate the result of first derivative again with respect to x,

$$ f’’(x) \;=\; \frac{d}{dx}(3x^2 - 6x + 2) $$

$$ f’’(x) \;=\; 6x - 6 $$

Apply the condition of the second derivative test to find relative maxima or minima values,

$$ For\; x_1 \;=\; 1 + \frac{\sqrt{3}}{3} $$

$$ f’’ \left(1 + \frac{\sqrt{3}}{3} \right) \;=\; 6 \left( 1 + \frac{\sqrt{3}}{3} \right) - 6 $$

$$ f’’ \left(1 + \frac{\sqrt{3}}{3} \right) \;=\; 6 + 2\sqrt{3} - 6 $$

$$ f’’ \left( 1 + \frac{\sqrt{3}}{3} \right) \;=\; 2\sqrt{3} > 0 $$

x1 is a local minimum.

$$ For\; x_2 \;=\; 1 - \frac{\sqrt{3}}{3} $$

$$ f’’ \left( 1 - \frac{\sqrt{3}}{3} \right) \;=\; 6 \left(1 - \frac{\sqrt{3}}{3} \right) - 6 $$

$$ f’’ \left(1 - \frac{\sqrt{3}}{3} \right) \;=\; 6 - 2\sqrt{3} - 6 $$

$$ f’’ \left(1 - \frac{\sqrt{3}}{3} \right) \;=\; -2\sqrt{3} < 0 $$

x2 is a local maximum.

Finally put the critical point value in the given function f(x),

$$ For\; x_1 \;=\; 1 + \frac{\sqrt{3}}{3} $$

$$ f \left(1 + \frac{\sqrt{3}}{3} \right) \;=\; \left(1 + \frac{\sqrt{3}}{3} \right)^3 - 3 \left(1 + \frac{\sqrt{3}}{3} \right)^2 + 2 \left(1 + \frac{\sqrt{3}}{3} \right) $$

$$ For\; x_2 \;=\; 1 - \frac{\sqrt{3}}{3} $$

$$ f \left(1 + \frac{\sqrt{3}}{3} \right) \;=\; \left(1 + \frac{\sqrt{3}}{3} \right)^3 - 3 \left(1 + \frac{\sqrt{3}}{3} \right)^2 + 2 \left( 1 + \frac{\sqrt{3}}{3} \right) $$

$$ For\; x_2 \;=\; 1 - \frac{\sqrt{3}}{3} $$

$$ f \left(1 - \frac{\sqrt{3}}{3} \right) \;=\; \left(1 - \frac{\sqrt{3}}{3} \right)^3 - 3 \left(1 - \frac{\sqrt{3}}{3} \right)^2 + 2 \left(1 - \frac{\sqrt{3}}{3} \right) $$

And simplify you get the solution of given function is,

$$ f(x_1) \;=\; f \left(1 + \frac{\sqrt{3}}{3} \right) \approx 0.816 $$

$$ f(x_2) \;=\; f \left(1 - \frac{\sqrt{3}}{3} \right) \approx -0.816 $$

Sketch a graph using local maxima or local minma value,

PASTE THE GRAPH HERE!

How to Use the Relative Extrema Calculator?

The saddle point calculator has an easy-to-use interface, so you can easily use it to evaluate the Extrema function questions for the graph. Before adding the input for the solutions of given function problem, you must follow our instructions. These instructions are:

1. Enter the given function value to find the extrema point in the input box.
2. Review your input value of the function for finding the local maxima or minima point in the extreme points calculator before hitting the calculate button to start the calculation process.
3. Click on the “Calculate” button to get the desired result of your given extrema function problem.
4. If you want to try out our extreme value calculator to check its accuracy in solution then use the load example
5. Click on the “Recalculate” button to get a new page for solving more functions and finding relative extrema points.

Final Result of Saddle Point Calculator:

The extreme values calculator gives you the solution to a given problem when you add the input to it. It provides you with solutions that may contain as:

• Result Option:

You can click on the result option and then the local extrema calculator provides you with a solution for the given differential function questions

• Possible Step:

When you click on the possible steps option it provides you with the solution of the extrema problem where all calculation steps are given in detail.

• Plot Option:

It gives you the solution of function in the form of a graph that gives you a graphical representation using extrema points on the graph.

Benefits of Using Extreme Points Calculator:

The extreme calculator gives you tons of benefits whenever you use it to calculate derivative graph problems and to get its solution immediately. These benefits are:

• Our extreme point calculator saves the time and effort that you consume in solving complex differential questions in a few seconds
• It is a free-of-cost tool that provides you the solution for a given derivation function to find its extrema points for graphical representation on a graph without paying a single penny.
• You can use this saddle point calculator for practice so that you get a strong hold on the Extrema Point method.
• It is a trustworthy tool that provides you with accurate solutions as per your input to calculate the extrema function problem.
• Global Extrema Calculator is a handy tool because you can use it for free online and get a solution to even a complex Extrema Point function easily.