- #1

Lancelot1

- 28

- 0

Hello everyone,

I am trying to solve this wee problem regarding partial derivatives, and not sure how to do so.

The following image shows level curves of some function \[z=f(x,y)\] :

View attachment 7998

I need to determine whether the following partial derivatives are positive or negative at the point P:

\[f_{x} , f_{y} , f_{xx} , f_{yy} , f_{xy} , f_{yx}\]

I am not sure how to relate the partial derivatives to the level curves. I know that partial derivatives at a point are slopes of a curve created when we fix a plane such as x=a or y=b. Where and how do I see it in level curves ?

Cheers !

I am trying to solve this wee problem regarding partial derivatives, and not sure how to do so.

The following image shows level curves of some function \[z=f(x,y)\] :

View attachment 7998

I need to determine whether the following partial derivatives are positive or negative at the point P:

\[f_{x} , f_{y} , f_{xx} , f_{yy} , f_{xy} , f_{yx}\]

I am not sure how to relate the partial derivatives to the level curves. I know that partial derivatives at a point are slopes of a curve created when we fix a plane such as x=a or y=b. Where and how do I see it in level curves ?

Cheers !