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 points

f (λ) = x^{2} - y^{2} - λ (4 x - 7 y - 10)

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})

5 x^{2}

y = 8 + x - x^{2}

f (x) = - (x + 2)^{5} (x - 4)^{4}

f (x, y) = x^{3} - 3 x + x y^{2}

f (x) = 3 x^{3} + 2 x^{2} - 10 x + 600

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)