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If x lies between -5 and 11, then the gr...

If `x` lies between `-5` and `11`, then the greatest value of `(11-x)^(3)(x+5)^(5)` is

A

`6^(5)*10^(3)`

B

`6^(3)*10^(3)`

C

`6^(3)*10^(4)`

D

`6^(3)*10^(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` Using weighted `A.M.` and `G.M.`
`(3((11-x)/(3))+5((x+5)/(5)))/(3+5) ge (((11-x)/(3))^(3)((x+5)/(5))^(5))^((1)/(3+5))`
`:. (11-x+x+5)/(8) ge (((11-x)^(3)(x+5)^(5))/(3^(3)*5^(5)))^(1//8)`
`:.(2)^(8) ge((11-x)^(3)(x+5)^(5))/(3^(3)*5^(5))`
`:. (11-x)^(3)(x+5)^(5) le 2^(8)*3^(3)*5^(5)`
`implies(11-x)^(3)(x+5)^(5) le 6^(3)*10^(5)`
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