Use Lagrange Multipliers to find the Maximum and Minimum values of f(x,y) = x2-y.
Subject to the restraint g(x,y) = x2+y2=25
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
x2+y2 = 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