What is the critical f(x,y)=4x^3+y^2-12x^2-8y+9x-2 ?

The critical f(x,y)=4x^3+y^2-12x^2-8y+9x-2 is (1/2 ,4),(3/2 ,4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

critical f(x,y)=4x^3+y^2-12x^2-8y+9x-2

critical points

f (x, y) = 4 x^{3} + y^{2} - 12 x^{2} - 8 y + 9 x - 2

(\frac{1}{2}, 4), (\frac{3}{2}, 4)

Solution steps

4 x^{3} + y^{2} - 12 x^{2} - 8 y + 9 x - 2

Find where

\nabla f (x, y)

is equal to zero or undefined

(\frac{1}{2}, 4), (\frac{3}{2}, 4)

f (x) = ∣ x ∣^{x}

f (x, y) = x y - x^{2} - y^{2} - 8 x - 2 y + 4

f (x, y) = x^{2} - 3 y^{2} - 8 x + 9 y + 3 x y

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

f (x) = 3 x^{2} + 4 x + 1

What is the critical f(x,y)=4x^3+y^2-12x^2-8y+9x-2 ?
The critical f(x,y)=4x^3+y^2-12x^2-8y+9x-2 is (1/2 ,4),(3/2 ,4)