Absolute Extrema Calculator

How to Use the Absolute Extrema Calculator

This guide will assist you in using the Absolute Extrema Calculator effectively to determine the absolute maximum and minimum values of a given function within a specified interval.

Step 1: Input the Function Expression

Start by entering the value of the function at various points. Ensure that these values are accurate representations of the function you are analyzing. This value will be used alongside other inputs to determine the extrema.

• Label: f(x)
• Type: Number
• Validation: Required

Step 2: Define the Interval

Next, you need to specify the interval within which you want to find the absolute extrema. This involves two sub-steps:

• Left Endpoint (a): Enter the lower limit of the interval.
  • Type: Number
  • Validation: Required
  • Step: 0.1
• Right Endpoint (b): Enter the upper limit of the interval.
  • Type: Number
  • Validation: Required
  • Step: 0.1

Step 3: Enter Critical Point(s)

Input any critical points of the function within the specified interval. These are points where the derivative of the function is zero or undefined. Enter them as accurately as possible to ensure correct calculation results.

• Label: Critical Point(s)
• Type: Number
• Validation: Required
• Step: 0.1

Step 4: Calculate the Results

After entering all the required values, the calculator will compute the absolute maximum and minimum values of the function within the specified interval, along with their respective locations.

• Absolute Maximum: The highest function value found (& with up to 4 decimal precision).
  • Calculation Logic: max(functionExpression, criticalPoints, leftEndpoint, rightEndpoint)
• Absolute Minimum: The lowest function value found (& with up to 4 decimal precision).
  • Calculation Logic: min(functionExpression, criticalPoints, leftEndpoint, rightEndpoint)
• Location of Maximum: The point at which the maximum value occurs (& with up to 4 decimal precision).
  • Calculation Logic: argmax(functionExpression, criticalPoints, leftEndpoint, rightEndpoint)
• Location of Minimum: The point at which the minimum value occurs (& with up to 4 decimal precision).
  • Calculation Logic: argmin(functionExpression, criticalPoints, leftEndpoint, rightEndpoint)

Review the results displayed for their correctness and use them as needed in your analysis or application.