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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

\begin{displaymath}
z = f(x_0,y_0)+ f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0).
\end{displaymath}

See also Normal Vector, Tangent, Tangent Line, Tangent Space, Tangent Vector




© 1996-9 Eric W. Weisstein
1999-05-26