Unformatted text preview: x = −→ x − −→ x . Note that in the de²nition above we are specifying where the tangent plane is being found by the value of the input −→ x ; when we regard the graph as simply a surface in space, we should really think of the plane at ( x,y ) = ( x ,y ) as the tangent plane at the point P ( x ,y ,z ) in space, where z = f ( x ,y ). For example, consider the function f ( x,y ) = x 2 − 3 y 2 2 : the partials are ∂f ∂x = x ∂f ∂y = − 3 y so taking −→ x = p 1 , 1 2 P , we ²nd f p 1 , 1 2 P = 1 8 ∂f ∂x p 1 , 1 2 P = 1 ∂f ∂y p 1 , 1 2 P = − 3 2...
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 Fall '08
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 Calculus, Derivative, Slope, Continuous function, Graph of a function

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