What is the extreme f(x,y)=-x^2+5y^2-7x+2y+5 ?

The extreme f(x,y)=-x^2+5y^2-7x+2y+5 is Saddle(-7/2 ,-1/5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=-x^2+5y^2-7x+2y+5

extreme points

f (x, y) = - x^{2} + 5 y^{2} - 7 x + 2 y + 5

Saddle (- \frac{7}{2}, - \frac{1}{5})

Solution steps

Find the critical points:

(- \frac{7}{2}, - \frac{1}{5})

\frac{\partial ^{2} f}{\partial x ^{2}} = 10

D (x, y) = - 20

Check the sign of at each critical point

Check critical point

(- \frac{7}{2}, - \frac{1}{5}) :

Saddle

Saddle (- \frac{7}{2}, - \frac{1}{5})

f (x, y) = - x^{3} + 4 x \cdot y - 2 y^{2} + 1

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

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

f (x) = x^{2} - 9, - 4 \leq x \leq 3

f (x, y) = x^{2} y - 15 x y^{2} + 12 y

What is the extreme f(x,y)=-x^2+5y^2-7x+2y+5 ?
The extreme f(x,y)=-x^2+5y^2-7x+2y+5 is Saddle(-7/2 ,-1/5)