Find slope of multivariable function

[dolle39]

Homework Statement

A hill is described with the following function:

f(x,y) = 3/(1+x2 +y2)

Where f(x,y) is the height. Find the points where the hill is steepest!

Homework Equations

∇f(x,y) = d/dx(f(x,y))i + d/dy(f(x,y))j

The Attempt at a Solution

d/dx(f(x,y)) = -6x/(1+x²+y²)²
d/dy(f(x,y)) = -6y/(1+x²+y²)²

Know as far as I understand the maximum slope should occur when:

||∇f(x,y)|| has it max. But how should I find that? And am I even going in the right direction?

 

[haruspex]

Yes, that should work. You can write out the expression for ||∇f(x,y)|| and differentiate wrt to x, y, to find out where its extremals are. You can make life a bit easier by noting that you can discard the square root operation, since a positive value is maximised when its square is maximised.