- #1

Kruum

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## Homework Statement

First problem: Let [tex]f(x,y) = x-y[/tex] and

**u**= v

**i**+w

**j**. In which direction does the function decrease and increase the most? And what

**u**(all of them) satisfies D

_{u}f = 0

Second problem: Let [tex]z = f(x,y)[/tex], where [tex]x = 2s+3t[/tex] and [tex]y = 3s-2t[/tex]. Determine [tex]\partial{z^2}/\partial{s^2}[/tex]

## Homework Equations

Gradient and the chain rule

## The Attempt at a Solution

For the first question in the first problem I've gotten using gradient: increase

**i**-

**j**and decrease -

**i**+

**j**. Am I correct? For the second question all I've gotten so far is (nabla)f(dot)

**u**= 0 = (1-y)v+(x-1)w. Where do I get the second equation to solve both v and w?

Second problem gives me 4z

_{xx}+12z

_{xy}+9z

_{yy}. Is that completely wrong?

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