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Gradients and directional derivatives

21c8b4e62805336faf3a9b7b280d1965.png

I can do part a and i know how to find the gradient vector but im really confused about the rest. Any help would be appreciated.
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mqb2766
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Original post by (1)Quantum
21c8b4e62805336faf3a9b7b280d1965.png

I can do part a and i know how to find the gradient vector but im really confused about the rest. Any help would be appreciated.


b) part 2, you have two simultaneous equations in x and y, both equal to zero. What curve(s) solve these equations?

c) Similar to b) except that only the df/dy = 0.

d) Evaluation at P is straightforward? Then evaulate the (scalar) gradient along the slice at 45 degrees.
Original post by (1)Quantum


I can do part a and i know how to find the gradient vector but im really confused about the rest. Any help would be appreciated.


For part (b), you're interested in the equations of curves in the x-y plane. This means z=f(x,y)=0z = f(x,y) = 0 is a requirement.

This is in addition to ∇f=0\nabla f = 0.

Don't have time to help with the rest at the moment, but (c) should be no trouble with the hint there!
Original post by RDKGames
For part (b), you're interested in the equations of curves in the x-y plane. This means z=f(x,y)=0z = f(x,y) = 0 is a requirement.

This is in addition to ∇f=0\nabla f = 0.


Perhaps I'm misunderstanding the question, but I don't see any need for the additional restriction, f(x,y)=0.

We're only interested in the solution to ∇f=0\nabla f=0 regardless of whether that solution is part of the level set f(x,y)=0. Are we not?
(edited 5 years ago)
Original post by ghostwalker
Perhaps I'm misunderstanding the question, but I don't see any need for the additional restriction, f(x,y)=0.

We're only interested in the solution to ∇f=0\nabla f=0 regardless of whether that solution is part of the level set f(x,y)=0. Are we not?


From first glance, the question asks for curves in the x-y plane so to me it seemed natural to impose the z=0z=0 condition.

But after having a further look into this question, it's clear to me that this going to prevent us from obtaining any solutions at all.

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