What is the extreme f(λ)=x^2-y^2-λ(4x-7y-10) ?

The extreme f(λ)=x^2-y^2-λ(4x-7y-10) is Saddle(2λ,(7λ)/2)

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extreme f(λ)=x^2-y^2-λ(4x-7y-10)

extreme

Saddle (2 λ, \frac{7 λ}{2})

Solution steps

Find the critical points:

(2 λ, \frac{7 λ}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 2

D (x, y) = - 4

Check the sign of at each critical point

Check critical point

(2 λ, \frac{7 λ}{2}) :

Saddle

Saddle (2 λ, \frac{7 λ}{2})

What is the extreme f(λ)=x^2-y^2-λ(4x-7y-10) ?
The extreme f(λ)=x^2-y^2-λ(4x-7y-10) is Saddle(2λ,(7λ)/2)