If the derivative of an analytic function f is 0, does that mean that the partial derivative of f with respect to x=0 and the partial derivative of f with respect to y=0? And conversely, suppose I know the partial derivates of a function are both equal to 0, can I then assume that the derivative of the function is 0?

If the derivative of an analytic function f is 0, does that mean that the partial derivative of f with respect to x=0 and the partial derivative of f with respect to y=0? And conversely, suppose I know the partial derivates of a function are both equal to 0, can I then assume that the derivative of the function is 0?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 29E

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