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Tangent Plane

The tangent plane to the graph of a function f differentiable at (x_0,y_0) is the nonvertical plane through the point (x_0,y_0,f(x_0,y_0)) given by

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

where f_x=partialf/partialx and f_y=partialf/partialy are the partial derivatives with respect to x and y, respectively (do Carmo 1976, Strang and Herman 2016).

See also

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

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References

do Carmo, M. P. "The Tangent Plane; The Differential of a Map." §2-4 in Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, p. 88, 1976.Strang, G. and Herman, E. "Tangent Planes and Linear Approximations." §4.4 in Calculus Volume 3. Houston, TX: OpenStax, 2016. https://openstax.org/books/calculus-volume-3/pages/4-4-tangent-planes-and-linear-approximations.

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Tangent Plane

Cite this as:

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

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