# Find and classify all the critical points of f(x,y) = x3+3x2-3x-y3+6y2-9y.  Find the maximum and minimum of f on the region x[-1,1], y[-1,1]

Question
Asked Mar 25, 2020
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Find and classify all the critical points of f(x,y) = x3+3x2-3x-y3+6y2-9y.  Find the maximum and minimum of f on the region x[-1,1], y[-1,1]

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Step 1

Find partial derivatives of the function f (x, y) = x3 + 3x2 - 3x – y3 + 6y2 – 9y with respect to x  and y.

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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