What is the extreme f(x,y)=(x-3)(y-3)(x+y-3) ?

The extreme f(x,y)=(x-3)(y-3)(x+y-3) is Saddle(3,0),Maximum(2,2)

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-3)(y-3)(x+y-3)

extreme points

f (x, y) = (x - 3) (y - 3) (x + y - 3)

Saddle (3, 0), Maximum (2, 2)

Solution steps

Find the critical points:

(3, 0), (2, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 (x - 3)

D (x, y) = - 4 x^{2} + 24 x - 4 x y + 24 y - 4 y^{2} - 45

Check the sign of at each critical point

Check critical point

(3, 0) :

Saddle

Check critical point

(2, 2) :

Maximum

Saddle (3, 0), Maximum (2, 2)

\frac{5 x - 3}{36 - x ^{2}}

f (x) = f (x) = x + \frac{25}{x} + 9, 1 \leq x \leq 50

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

f (x, y) = x^{2} - 6 x y + 2 y^{2} + 10 x + 2 y - 5

\frac{3}{4} \times \frac{2}{5}

What is the extreme f(x,y)=(x-3)(y-3)(x+y-3) ?
The extreme f(x,y)=(x-3)(y-3)(x+y-3) is Saddle(3,0),Maximum(2,2)