find local minima of function f(x,y) = 1 + x^2 + y^2 - 4xy
How do I find the
To be more specific, I am trying to find local minima of function f(x,y) = 1 + x^2 + y^2 - 4xy
When I compute the partial derivatives:
fx(x,y) = 2x - 4y
fy(x,y) = 2y - 4x
fxx = 2
fyy = 2
fxy = -4
To get the discriminant then:
D = fxx * fyy -(fxy)^2
D = 2*2-(-4)^2 = -12
Since D < 0, this is a saddle point. However there are actually no points included, this value is computed from the fixed derivatives which turn into constants.
How do I then find specifically the local minima of a function like this?
Later there is also a constraint g(x,y) = x^2 + y^3 - 2 = 0, but it should be possible to arrive at the minima without this as well according to the question.
Step by step
Solved in 3 steps