Question

basic lagrange multiplier question! maximum/minimum of \(f(x,y)=x^2-y^2\) subject to \(x^2+y^2=2\)

Answer 1

hmm...Constrained Optimization

Answer 2

Start by taking the gradient of both functions...
\[\nabla f(x,y)=2x i-2yj\]\[\lambda\nabla g(x,y)=2x \lambda i+2y \lambda j \]
\[2x=2xλ\]\[\lambda=1\]\[-2y=2yλ\]\[\lambda=-1\]

Answer 3

that's where I am stuck