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Consider the region R= \(x,y):x y 9- 113x2, x 0 \. The area of the largest rectangle of sides parallel to the coordinate axes and inscribed in R, is:
(2) 567121
Largest rectangle: left side on the y-axis, right side at x=t.
[figure]
Height =9- 113t2-t, so A=9t-t2- 113t3
A'=9-2t-11t2=0 (11t-9)(t+1)=0 t= 911
A = 911 (9- 2711- 911 )= 911 6311= 567121
Answer: (2)
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