rev3 - gives or , and then . The fact that this gives a...

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f (x,y)= xy 36 ± 9 x 2 ± 36 y 2 ( ) 1/2 /2 x,y,z ( ) f x = y 36 ± 9 x 2 ± 36 y 2 ( ) 1/2 2 + ± 9 x 2 y 36 ± 9 x 2 ± 36 y 2 ( ) ± 1/2 2 = 36 y ± 18 x 2 y ± 36 y 3 ( ) 2 36 ± 9 x 2 ± 36 y 2 ( ) 1/2 f y = 36 x ± 9 x 3 ± 72 xy 2 2 36 ± 9 x 2 ± 36 y 2 ( ) 1/2 f x =0 y =0 y 2 = 2 ± x 2 2 y >0 y f y =0 x 2 = 4 3 x = 2 3 y = 1 3 z 2 =(36 ± 12 ± 12)/4=3 V =(2 x )(2 y )(2 z )=8 2 3 1 3 3 ( ) = 16 3 43. Maximize with in first octant. Then and . Setting gives or but , so only the latter solution applies. Substituting this into
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Unformatted text preview: gives or , and then . The fact that this gives a maximum volume follows from the geometry. This maximum volume is . 1 Stewart Calculus ET 5e 0534393217;14. Partial Derivatives; 14.7 Maximum and Minimum Values...
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