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For z=f(x,y) , in the stationary points, the partial derivatives with respect to x and y are both 0. But are all the directional derivatives of the stationary points zero as well? Why do we only care about partial derivatives rather than directional derivatives?

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  • $\begingroup$ If the function is differentiable at that point then directional derivative is just the inner product of a vector (direction) with the gradient (vector of partial derivatives) so if the gradient is 0 the directional derivative is 0 as well. $\endgroup$ – RozaTh Oct 24 '18 at 16:55

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