What is the extreme (x^2-5x)(y^2-8y) ?

The extreme (x^2-5x)(y^2-8y) is Saddle(0,8),Saddle(5,8),Saddle(0,0),Saddle(5,0),Maximum(5/2 ,4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme (x^2-5x)(y^2-8y)

extreme points

(x^{2} - 5 x) (y^{2} - 8 y)

Saddle (0, 8), Saddle (5, 8), Saddle (0, 0), Saddle (5, 0), Maximum (\frac{5}{2}, 4)

Solution steps

Find the critical points:

(0, 8), (5, 8), (0, 0), (5, 0), (\frac{5}{2}, 4)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 (x^{2} - 5 x)

D (x, y) = - 12 x^{2} y^{2} + 96 x^{2} y - 256 x^{2} + 60 x y^{2} - 480 x y + 1280 x - 100 y^{2} + 800 y - 1600

Check the sign of at each critical point

Check critical point

(0, 8) :

Saddle

Check critical point

(5, 8) :

Saddle

Check critical point

(0, 0) :

Saddle

Check critical point

(5, 0) :

Saddle

Check critical point

(\frac{5}{2}, 4) :

Maximum

Saddle (0, 8), Saddle (5, 8), Saddle (0, 0), Saddle (5, 0), Maximum (\frac{5}{2}, 4)

T (x, y) = 10 - 2 x^{2} - 3 y^{2}

f (x) = e^{4 x^{2} + 2 y^{2} - 32 x}

f (x, y) = x y (8 + x) (y - 9)

\frac{3}{2} x^{2} + x y + \frac{1}{108} y^{4}

(3 x - 4)^{2}

What is the extreme (x^2-5x)(y^2-8y) ?
The extreme (x^2-5x)(y^2-8y) is Saddle(0,8),Saddle(5,8),Saddle(0,0),Saddle(5,0),Maximum(5/2 ,4)