Local Extremum – A function with fixed powers – Exercise 5523

Exercise

Given the function

z=xy+x22y29yz=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,xy8=0x=0, y=0, x-y-8=0

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

Final Answer

A saddle point

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

Min and max values

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

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

Solution

Coming soon…

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