What is the critical f(x,y)=x^3+12xy^2-15x-24y ?

The critical f(x,y)=x^3+12xy^2-15x-24y is (1,1),(-1,-1),(2, 1/2),(-2,-1/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

critical f(x,y)=x^3+12xy^2-15x-24y

critical points

f (x, y) = x^{3} + 12 x y^{2} - 15 x - 24 y

(1, 1), (- 1, - 1), (2, \frac{1}{2}), (- 2, - \frac{1}{2})

Solution steps

x^{3} + 12 x y^{2} - 15 x - 24 y

Find where

\nabla f (x, y)

is equal to zero or undefined

(1, 1), (- 1, - 1), (2, \frac{1}{2}), (- 2, - \frac{1}{2})

x^{\frac{2}{3}}

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

f (x) = - 2 e^{- 2 x} (x^{4} - 2 x^{3})

f (x) = 2 x^{3} - 3 x^{2} - 12 x + 15

f (x) = (x - 1)^{2} (x - 3)^{2}

What is the critical f(x,y)=x^3+12xy^2-15x-24y ?
The critical f(x,y)=x^3+12xy^2-15x-24y is (1,1),(-1,-1),(2, 1/2),(-2,-1/2)