Relative Extrema Calculator

How to Use the Relative Extrema Calculator

Introduction

The Relative Extrema Calculator is designed to help you find the key points of interest, such as local and absolute extrema and inflection points, of a given mathematical function. Follow the steps below to use this tool effectively for either polynomial or trigonometric functions.

Step-by-Step Guide

Step 1: Select the Function Type

Begin by selecting the type of function you want to analyze. The calculator supports two types of functions:

• Polynomial: A function represented by a polynomial equation.
• Trigonometric: A function that involves trigonometric identities like sine and cosine.

Step 2: Enter the Degree of the Polynomial (if applicable)

If you selected the Polynomial option in the previous step, you need to specify the degree of the polynomial. Enter a number between 1 and 6, as these are the supported degrees for analysis by the calculator.

Step 3: Specify the Range of X Values

Enter the range over which you want the calculator to find extrema and inflection points. Provide the following:

• Start X Value: The starting x-value of the range. This value must be between -100 and 100.
• End X Value: The ending x-value of the range. This value must also be between -100 and 100.

Ensure that the end x-value is greater than the start x-value to define a valid range.

Step 4: Interpret the Results

Once all the fields are filled out, the calculator will provide the following points of interest:

• Local Maximum Points: Points where the function reaches a local maximum within the specified range, formatted as (x, y).
• Local Minimum Points: Points where the function reaches a local minimum within the specified range, formatted as (x, y).
• Absolute Maximum: The highest y-value of the function in the given range, formatted as y = value.
• Absolute Minimum: The lowest y-value of the function in the given range, formatted as y = value.
• Inflection Points: Points where the function changes concavity, formatted as (x, y).

Conclusion

By following the above steps, you can effectively use the Relative Extrema Calculator to analyze polynomial and trigonometric functions within a given range. Ensure all input values are set as required by the calculator to obtain accurate results.