Use this tangent plane calculator to swiftly find the equation of a tangent plane to a surface at a given point.

Tangent Plane Calculator

Use this calculator to find the equation of the tangent plane to the function f(x, y) at a given point (a, b).

How to Use the Calculator

Input the function f(x,y) in terms of x and y where the tangent plane is to be found. Then, provide the x-coordinate (a) and y-coordinate (b) of the point. Press the “Calculate” button to obtain the equation of the tangent plane.

How the Calculator Works

The calculator computes the partial derivatives of the function with respect to x and y at the given point (a, b) using a method of finite differences. It then uses these derivatives to construct the equation of the tangent plane in the form z = f(a, b) + f_x(a, b) * (x – a) + f_y(a, b) * (y – b), where f_x and f_y are the partial derivatives at the point (a, b).

Limitations

Please note that this calculator uses numerical differentiation which may not be accurate for functions with complex behavior near the point of tangency or for points very close to singularities or discontinuities of the function. For best results, ensure the function is smooth and well-behaved at and around the point of tangency.