What is the extreme f(x,y)=3x^2-y^2-7x-y+8 ?

The extreme f(x,y)=3x^2-y^2-7x-y+8 is Saddle(7/6 ,-1/2)

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extreme f(x,y)=3x^2-y^2-7x-y+8

extreme points

f (x, y) = 3 x^{2} - y^{2} - 7 x - y + 8

Saddle (\frac{7}{6}, - \frac{1}{2})

Solution steps

Find the critical points:

(\frac{7}{6}, - \frac{1}{2})

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

D (x, y) = - 12

Check the sign of at each critical point

Check critical point

(\frac{7}{6}, - \frac{1}{2}) :

Saddle

Saddle (\frac{7}{6}, - \frac{1}{2})

f (x) = 2 + 28 x - 2 x^{2}

f (x) = 2 x^{3} - x^{2} - 4 x + 10, - 1 \leq x \leq 0

f (x) = - \frac{4}{3} x^{\frac{3}{4}}

2 sin (\frac{θ}{2})

f (x) = 4 + 8 x + 128 x^{- 1}

What is the extreme f(x,y)=3x^2-y^2-7x-y+8 ?
The extreme f(x,y)=3x^2-y^2-7x-y+8 is Saddle(7/6 ,-1/2)