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Find the maximum and minimum values of : $x^3+3xy^2-3x^2-3y^2+4$
1 Answer
written 7.9 years ago by | • modified 7.9 years ago |
Let, $ f(x,y)=x^3+3xy^2-3x^2-3y^2+4 \\ \; \\ $
The stationary points are given by $\dfrac{\partial u}{\partial x}=0 $ and $\dfrac{\partial u}{\partial y}=0$
$ \\ \; \\ \therefore \dfrac{\partial u}{\partial x} \;=\; 3x^2+3y^2-6x=0 \; \; \; \therefore x^2+y^2-2x=0 \; \; \ldots(i) \\ $
Also, $ \\ \; \\ \therefore \dfrac{\partial u}{\partial y} …