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Maximum and minimum values
written 2.6 years ago by | modified 2.6 years ago by |
Find the maximum and minimum values of x 3 + 3xy 2 – 3x 2 – 3y 2 + 7.
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written 2.6 years ago by | modified 2.6 years ago by |
Find the maximum and minimum values of x 3 + 3xy 2 – 3x 2 – 3y 2 + 7.
written 2.6 years ago by |
Let, $ f(x,y)=x^3+3xy^2-3x^2-3y^2+7 \\ \; \\ $
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} …