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Differentiable function

The function f(x) is differentiable at a if the limitMATH exists. If f is differentiable at a, then the tangent line to the graph of f at a is given by y = f '(a)(x - a) + f(a)

The function f(x, y) is differentiable at  (a, b) if we can write f(x,y) = f(a,b) + fx(a,b)(x - a) + fy(a,b)(y - b) + h(x - a) + k(y - b) where (h,k) → (0,0)  as (x,y) → (a,b) .

If f is differentiable at (a, b), then the tangent plane to the graph of f  at (a, b) is given by  z = f(a,b) + fx(a,b)(x - a) + fy(a,b)(y - b)


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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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