Represent the level curves

[sp4rrow]

Dear all,

Currently we are processing below topics but im confused about red area, how can i reach ▼f(1,0)=(2,0)?

 

[BigBeachBanana]

Dear all,

Currently we are processing below topics but im confused about red area, how can i reach ▼f(1,0)=(2,0)?

View attachment 36538

Plug in [imath](1,0)[/imath] into [imath]<2x,2y>[/imath] (the gradient vector).

 

[Dr.Peterson]

Dear all,

Currently we are processing below topics but im confused about red area, how can i reach ▼f(1,0)=(2,0)?

View attachment 36538

It isn't clear what you are trying to do; what do you mean by "reach"? It doesn't seem related to your title: determining that [imath]\nabla f(1,0)=(2,0)[/imath] isn't the same as "representing the level curves".

Please quote the problem as given to you; if that is what you did, please interpret it for us, and tell us what part of the problem you do understand, by showing your work.

As I see it, you (or someone else?) have drawn the level curve passing through each of these four points; and you can "check orthogonality", if that means verifying that the vectors you made are all orthogonal to the level curve, by drawing the vectors at their appropriate locations and visually observing this relationship, or perhaps by finding the slope, or tangent vector, of that curve at each point.