Extrema Calculator

The Extrema Calculator allows users to calculate and find local and absolute maxima and minima points and values for polynomial and trigonometric functions within a specified interval.

Use Our Extrema Calculator

How to Use the Extrema Calculator

Step 1: Select the Function

Start by selecting the type of function you want to analyze for extrema. You have two options:

  • Polynomial (ax² + bx + c) – Choose this for quadratic functions.
  • Trigonometric (a*sin(bx) + c) – Choose this for trigonometric functions.

Step 2: Enter Coefficients

Based on your function selection, input the relevant coefficients:

  • Coefficient a: Enter a value between -100 and 100. This coefficient is required.
  • Coefficient b: Enter a value between -100 and 100. This coefficient is required.
  • Coefficient c: Enter a value between -100 and 100. This coefficient is required.

Step 3: Define the Interval

Specify the interval over which you want to find the extrema:

  • Interval Start: Enter the starting value of the interval. The value must be between -100 and 100.
  • Interval End: Enter the ending value of the interval. The value must be between -100 and 100.

Step 4: Calculate Local Extrema

The calculator will compute the local maximum and minimum points using the formulas provided for your selected function:

  • Local Maximum Point – For polynomials, calculated using -b/(2a); for trigonometric functions, calculated using pi/(2b).
  • Local Maximum Value – For polynomials, calculated using (-b²/(4a) + c); for trigonometric functions, calculated using a*sin(b*localMaxima) + c.
  • Local Minimum Point – For polynomials, calculated like the maximum; for trigonometric functions, calculated using (3pi)/(2b).
  • Local Minimum Value – Calculated similarly to the maximum value, substituting localMinima where relevant.

Step 5: Calculate Absolute Extrema

The calculator will then compute the absolute maximum and minimum values over the specified interval:

  • Absolute Maximum – The highest value among the local maximum, function value at interval start, and function value at interval end.
  • Absolute Minimum – The lowest value among the local minimum, function value at interval start, and function value at interval end.

Review the results displayed to understand the extrema of your selected function within the given interval.