What is the critical f(x,y)=2x^3-21x^2+y^3+12y^2 ?

The critical f(x,y)=2x^3-21x^2+y^3+12y^2 is (0,0),(0,-8),(7,0),(7,-8)

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critical f(x,y)=2x^3-21x^2+y^3+12y^2

critical points

f (x, y) = 2 x^{3} - 21 x^{2} + y^{3} + 12 y^{2}

(0, 0), (0, - 8), (7, 0), (7, - 8)

Solution steps

2 x^{3} - 21 x^{2} + y^{3} + 12 y^{2}

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 0), (0, - 8), (7, 0), (7, - 8)

f (x) = e^{x^{2} - 8 x - 1}

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

f (x) = \frac{x ^{2} + 4}{x}

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

\frac{x ^{2} - 4}{1 - x ^{2}}

What is the critical f(x,y)=2x^3-21x^2+y^3+12y^2 ?
The critical f(x,y)=2x^3-21x^2+y^3+12y^2 is (0,0),(0,-8),(7,0),(7,-8)