Question

Asked Mar 25, 2020

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Find and classify all the critical points of f(x,y) = x^{3}+3x^{2}-3x-y^{3}+6y^{2}-9y. Find the maximum and minimum of f on the region x[-1,1], y[-1,1]

Step 1

Find partial derivatives of the function ** f (x, y) = x^{3} + 3x^{2} - 3x – y^{3 }+ 6y^{2 }– 9y **with respect to

Step 2

We have to find the maximum and minimum of function on the region ** x [-1,1], y [-1,1]**:

* *

There is only one point of the given domain which is a critical point:

Step 3

This point is the minimum point of the function and the minimum value of the function is:

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