Tangent Line Calculator

How to Use the Tangent Line Calculator

This guide will help you utilize the Tangent Line Calculator to determine the tangent line equation, the slope at a point, and the y-value on the given function at a specified x-value.

Step 1: Enter the x-value

The first step is to input the x-value at which you want to find the tangent line. This is the point of tangency on your chosen function. Locate the field labeled ‘x-value (point of tangency)’ and enter the desired x-value there. Ensure that you adhere to the validation rules by providing a value with increments of 0.1, as this input is required.

Step 2: Select the Function Type

Next, choose the type of function for which you wish to calculate the tangent line. This calculator provides options for linear, quadratic, exponential, sine, and cosine functions. Use the dropdown menu under the field labeled ‘Function Type’ to select the appropriate function type. This field is mandatory, so ensure you make a selection.

Step 3: Input Coefficients

For linear and quadratic functions, you must provide the coefficients for calculations to proceed correctly. Enter the values for ‘Coefficient a’ and ‘Coefficient b’ as prompted. These fields are required, and each must follow the defined validation with increments of 0.1 for precision in calculations.

Step 4: Calculate the Result

• Slope of Tangent Line: The calculator will compute the slope of the tangent line at the specified x-value based on the chosen function type. The formula varies:
  • Linear: Uses coefficient a directly.
  • Quadratic: Computes using 2 * a * x + b.
  • Exponential: Uses the exponential function e^x.
  • Sine: Uses the cosine function, cos(x).
  • Cosine: Uses the negative sine function, -sin(x).
• y-value at Point of Tangency: The calculator determines the y-value using the provided x-value and coefficients:
  • Linear: By a * x + b.
  • Quadratic: Uses a * x² + b * x.
  • Exponential: Using e^x.
  • Sine: By sin(x).
  • Cosine: By cos(x).
• Tangent Line Equation: Finally, the calculator will generate the equation of the tangent line formatted as y = slope(x - xValue) + yPoint.

Carefully review the calculated results provided in four decimal precision for the slope, the y-value, and the tangent line equation, to ensure they meet your needs.