On the region x + y² < 9, x > 0, y > 0, the function f(x, y) = xy²%3Dhasa) its absolute maximum of 6/3 and its absolute minimum of 0O b) its absolute maximum of 6V3 and its absolute minimum of6/3-O c) None of thesed) its absolute maximum of 3/3 and its absolute minimum of 0

To find the absolute maximum and absolute minimum of the function f(x,y) in the given region.

Answered: On the region x2 + y° < 9, x > 0, y >…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?

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How are the absolute maximum and minimum similar to and different from the local extrema?
When finding the maximum and minimum values of the function z = xy - 2y - 2x on the region bounded by the triangle with vertices (2,0), (1,6), and (4,4), one only has to check the values of the function at six points: the three vertices, two other boundary points, and one interior point. Let the values of the function at those points be z₁, Z2, Z3, Z4, Z5, and z6. Let the maximum of the function z on the triangle be M and the minimum be m. Then the value of cos z₁ + cos z2 + cos z3 + cos Z4 + cos z5 + cos z6 + sin m + sin M is (A) 0.0104572 (B) -2.42308 (C) -1.1148 (D) -4.62857 (E) 3.84684 (F) 0.576989 (G) 0.335642 (H) 1.5793
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On the region x2 + y° < 9, x > 0, y > 0, the function f(x, y) = xy has O a) its absolute maximum of 6/3 and its absolute minimum of 0 O b) its absolute maximum of 6/3 and its absolute minimum of -6V3 c) None of these d) its absolute maximum of 3/3 and its absolute minimum of 0