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20 is divided into two parts so that pro...

20 is divided into two parts so that product of cube of one quantity and square of the other quantity is maximum. The parts are

A

10, 10

B

16, 4

C

8, 12

D

12, 8

Text Solution

Verified by Experts

The correct Answer is:
D
Let `x+y=20impliesy=20y=20-x`
and `x^(3).y^(2)=zimpliesz=x^(3).y^(2)`
`z=x^(3)(20-x)^(2)impliesz=400x^(3)+x^(5)-40x^(4)`
`(dz)/(dx)=1200x^(2)+5x^(4)-160x^(3)`
Now `(dz)/(dx)=0`, Then `x=12,20`
Now `(d^(2)z)/(dx^(2))=2400x+16x^(3)-480x^(2),((d^(2)x)/(dx^(2)))_(x=12)=-ive`
Hence `x=12` is the point of maxima
`x=12,y=8`.
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