(1) Let [itex]f(x)=x^3+y^3+z^3-3xyz[/itex], Find grad(f).(adsbygoogle = window.adsbygoogle || []).push({});

[itex]grad(f)=(3x^2-3yz, 3y^2-3xz, 3z^2-3xy)[/itex].

(2) Identify the points at which grad(f) is

a) orthogonal to the z-axis

b) parallel to the x-axis

c) zero.

I have managed to solve for (1), but don't have a clue how to solve for the second part. I have not come across about the theory of "orthogonal to z-axis" and "parallel to x-axis", tried to look up on the internet but still quite confused.

However, for (c) I have come up with something like [itex]grad(f)=(3x^2-3yz, 3y^2-3xz, 3z^2-3xy)=(0,0,0)[/itex], so the points at which grad(f)=0 are (0,0,0). Is that right?

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# Homework Help: Gradient operator of a function

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