SOLUTION: Separate the number 11 into two parts such that the product of one part and the square of the other part is a maximum.
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Question 1074407: Separate the number 11 into two parts such that the product of one part and the square of the other part is a maximum. Answer by sachi(548) (Show Source):
You can put this solution on YOUR website! Separate the number 11 into two parts such that the product of one part and the square of the other part is a maximum.
let one part is x
so the other part is 11-x
As per qn (11-x)x^2 is maximum
now let f(x)=(11-x)x^2
f'(x)=22x-3x^2
for critical points f'(x)=0
this gives x= 0 or 22/3
now f"(x)=22-6x
so f"(0)=22 >0
& f"(22/3)=-22 <0
so for x=22/3 the f(x)is maximum
so one part is 22/3 & the other part is 11/3
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