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## Homework Statement

f(x,y)=y-x

i) compute the gradient

ii) at the given point (2,1) compute the gradient vector gradf(2,1)

iii) compute the level curve that passes through the point (2,1)

iiii) on the xy-plane, sketch the level curve from iii and the gradient vector gradf(2,1) you found in ii. Verify that they meet orthogonally

## Homework Equations

gradients, derivatives, etc.

## The Attempt at a Solution

I was out sick all last week from class so I need a little leg up on what we are doing...

for i) wouldn't this just be <-1,1> ?

and if so, I'm a little confused on ii) which I assumed to be <-1,1> still regardless of what point it was 'evaluated' at.

And then from here I'm not sure how to compute the level curve for this. Am I looking for a vector, equation, scalar? Before this when we talked about level curves in class, we were always given a set of constants to set them equal to.

And as far as iiii) goes, I'm a bit confused what this is supposed to look like since ii) would always be the vector <-1,1>