# Local Extremum – A function with fixed powers – Exercise 5523

Exercise

Given the function

$$z=xy+x^2-2y^2-9y$$

1. Find the local extremum points of the function and classify their type.

2. In the domain bounded by the lines

$$x=0, y=0, x-y-8=0$$

Find the maximum value and the minimum value of the function.

$$(1,-2,9)$$

Min and max values

$$\max_D z(8,0) = 64$$

$$\min_D z(0,-8) =-56$$

Solution

Coming soon…

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