SOLUTION: Separate the number 14 into two parts such that the product of one part and the square of the other part is a maximum.

Question 1074408: Separate the number 14 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 14 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 14-x
As per qn (14-x)x^2 is maximum
now let f(x)=(14-x)x^2
f'(x)=28x-3x^2
for critical points f'(x)=0
this gives x= 0 or 28/3
now f"(x)=28-6x
so f"(0)=28 >0
& f"(28/3)=-28 <0
so for x=28/3 the f(x)is maximum
so one part is 28/3 & the other part is 14/3
ans
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