What is a Tangent Plane?

A tangent plane is a flat surface that touches a curved surface at a single point without intersecting it. In multivariable calculus, it represents the best linear approximation of a function near a given point.

The tangent plane is crucial for understanding the local behavior of surfaces and functions in three-dimensional space.

How to Use the Tangent Plane Calculator?

1. Enter the Function

In the “Function” field, input the equation of the surface. You can use two formats:

Implicit function: e.g., x^2 + y^2 + z^2 = 14

Explicit function: e.g., z = x^2 + y^2

2. Specify the Point

In the “Point” field, enter the coordinates where you want to find the tangent plane:

For implicit functions, use the format: x,y,z (e.g., 1,3,2)

For explicit functions, you can use either x,y or x,y,z (e.g., 1,3 or 1,3,2)

3. Calculate

Click the “Calculate Tangent Plane” button to get the result. The calculator will display:

• The equation of the tangent plane
• A brief explanation of what the equation represents

The tool handles both implicit and explicit functions, making it versatile for various mathematical scenarios. It uses partial derivatives to compute the tangent plane equation, simplifying the result for easy interpretation.

This calculator is particularly useful for students studying multivariable calculus, engineers working with 3D modeling, and anyone dealing with surface analysis. It simplifies the process of finding tangent planes, which can be tedious and error-prone when done manually.