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

Options

A. `6^(5)*10^(3)`
B. `6^(3)*10^(3)`
C. `6^(3)*10^(4)`
D. `6^(3)*10^(5)`

Answer

D

Explanation

`(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)`