What is the critical S(A,B)=3A^4B^3-12B^3+7A^2 ?

The critical S(A,B)=3A^4B^3-12B^3+7A^2 is (0,0),(-sqrt(2),-\sqrt[3]{7/12}),(sqrt(2),-\sqrt[3]{7/12})

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critical S(A,B)=3A^4B^3-12B^3+7A^2

critical points

S (A, B) = 3 A^{4} B^{3} - 12 B^{3} + 7 A^{2}

Solution steps

3 A^{4} B^{3} - 12 B^{3} + 7 A^{2}

Find where

\nabla f (A, B)

is equal to zero or undefined

f (x) = x - 2 + 4 - x

f (x) = x^{\frac{4}{5}} (x - 8)^{2}

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

\frac{1}{4} x^{4} - x^{3} - 4 x + 2

f (x) = x^{2} - 4 x + 5

What is the critical S(A,B)=3A^4B^3-12B^3+7A^2 ?
The critical S(A,B)=3A^4B^3-12B^3+7A^2 is (0,0),(-sqrt(2),-\sqrt[3]{7/12}),(sqrt(2),-\sqrt[3]{7/12})