What is the critical f(x,y)=4xy-y^4-2x^2 ?

The critical f(x,y)=4xy-y^4-2x^2 is (0,0),(-1,-1),(1,1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

critical f(x,y)=4xy-y^4-2x^2

critical points

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

(0, 0), (- 1, - 1), (1, 1)

Solution steps

4 x y - y^{4} - 2 x^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (- 1, - 1), (1, 1)

x^{4} + x^{2} - 6 x y + 3 y^{2}

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

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

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

f (x) = x^{2} + 3 x y + 4 y^{2} - 6 x + 2 y

What is the critical f(x,y)=4xy-y^4-2x^2 ?
The critical f(x,y)=4xy-y^4-2x^2 is (0,0),(-1,-1),(1,1)