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

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

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

critical points

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

(1, 2), (- 1, - 2), (2, 1), (- 2, - 1)

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(1, 2), (- 1, - 2), (2, 1), (- 2, - 1)

7 + 2 x + 4 y - x^{2} - 4 y^{2}

- x^{2} - 4 x + 9

\frac{( x ^{3} )}{x ^{2} - 1}

(7 x + 5) e^{- 6 x}

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

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