What is the extreme f(x,y)=sqrt(144-9x^2-16y^2) ?

The extreme f(x,y)=sqrt(144-9x^2-16y^2) is Maximum(0,0)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x,y)=sqrt(144-9x^2-16y^2)

extreme points

f (x, y) = 144 - 9 x^{2} - 16 y^{2}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = - \frac{16 ( 144 - 9 x ^{2} )}{( 144 - 9 x ^{2} - 16 y ^{2} ) 144 - 9 x ^{2} - 16 y ^{2}}

D (x, y) = \frac{20736}{( 144 - 9 x ^{2} - 16 y ^{2} ) ^{2}}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = 24 x^{3} - 3 x^{4}

3 x^{2} - 12 x y + y^{3} + 3 y^{2}

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

1 + \frac{7}{x} - \frac{3}{x ^{2}}

f (x) = \frac{x}{x ^{2} + 1}, - 2 \leq x \leq 2

What is the extreme f(x,y)=sqrt(144-9x^2-16y^2) ?
The extreme f(x,y)=sqrt(144-9x^2-16y^2) is Maximum(0,0)