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

The critical f(x)=x^3-2x(y-4)+(y-4)^3 is (0,4),(2/3 , 14/3)

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critical f(x)=x^3-2x(y-4)+(y-4)^3

critical points

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

(0, 4), (\frac{2}{3}, \frac{14}{3})

Solution steps

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

Find where

\nabla f (x, y)

is equal to zero or undefined

(0, 4), (\frac{2}{3}, \frac{14}{3})

f (x) = x^{2} + \frac{1}{x ^{2}}

f (x) = 4 - 2 x^{3} - 2 y^{3} + 24 x + 6 y

y = x e^{- k x}

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

f (x) = (ln (x))^{2}

What is the critical f(x)=x^3-2x(y-4)+(y-4)^3 ?
The critical f(x)=x^3-2x(y-4)+(y-4)^3 is (0,4),(2/3 , 14/3)