Function Calculator

The Function Calculator allows users to calculate and analyze the values and derivatives of various mathematical functions, including linear, quadratic, exponential, and logarithmic, based on user input values and coefficients.

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How to Use the Function Calculator

This guide will provide step-by-step instructions on how to effectively use the Function Calculator. This tool allows you to compute the value of a function, its derivative at a specific point, and view the function’s expression.

Step 1: Input X Value

  1. Locate the input field labeled X Value.
  2. Enter a numerical value for X. This value must be between -1000 and 1000, with increments allowed every 0.1 unit.
  3. Ensure that the field is filled, as it is required for calculations to proceed.

Step 2: Select Function Type

  1. Find the dropdown labeled Function Type.
  2. Choose one of the following function types from the list:
    • Linear (ax + b)
    • Quadratic (ax² + bx + c)
    • Exponential (aᵇˣ)
    • Logarithmic (a·ln(x) + b)
  3. This field is required and must be selected for the calculator to work correctly.

Step 3: Enter Coefficients

  1. Input the following coefficients in their respective fields. Each field requires a value:
    • Coefficient a: Enter a value between -100 and 100 in increments of 0.1. This field is mandatory.
    • Coefficient b: Similarly, enter a value between -100 and 100 in increments of 0.1. This field is mandatory.
    • Coefficient c (for quadratic): Only enter a value if you have selected the quadratic function type. This is optional but follows the same validation rules as other coefficients.

Step 4: Interpret the Results

  1. After entering all the required inputs, the calculator will automatically display the results in the following fields:
    • Y Value: This field displays the computed value of the function based on the inputs provided. The result will be formatted to four decimal places.
    • Derivative at X: Here, you can view the derivative of the selected function at the entered X Value. This result will also be formatted to four decimal places.
    • Function Expression: The calculator will show the formula of the function used, displayed with a prefix as ‘f(x) =’.

By following these steps, you will be able to utilize the Function Calculator to evaluate different mathematical functions, their derivatives, and observe their mathematical expressions effectively.