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Tangent Plane

Let (x_0,y_0) be any point of a surface function z=f(x,y). Then the surface has a nonvertical tangent plane at (x_0,y_0) with equation

z=f(x_0,y_0)+f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0).

See also

Normal Vector, Plane, Tangent, Tangent Line, Tangent Space, Tangent Vector

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Cite this as:

Weisstein, Eric W. "Tangent Plane." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangentPlane.html

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