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## Homework Statement

Use Lagrange Multipliers to find the Maximum and Minimum values of f(x,y) = x

^{2}-y.

Subject to the restraint g(x,y) = x

^{2}+y

^{2}=25

## Homework Equations

gradient f(x,y)= gradient g(x,y)

## The Attempt at a Solution

I have found the gradients of f and g to be

f(x,y) = 2xi + -1j

g(x,y) = 2xi + 2yj

I have put these to gether with the constraint to find the simutaneous equation

2x = lambda 2x

-1 = lambda 2y

x

^{2}+y

^{2}= 25

Have I got this system right so far ?

I'm a bit concerned about the 2x = lambda 2x part.

I'm not sure if this is right or I should have used 2x = lambda 2y ?

In the original system I have Lambda = 1 and y = -1/2

Any help greatly appreciated

Brendan