Find the maximum value of `(7-x)^4(2+x)^5w h e nx` lies between `-2a n d7.`

Explanation

Since `- 2 lt x lt 7`
`:. X + 2 gt 0` and `7 - x gt 0`
We have to find maximum value of `(7 - x)^(4) (2 + x)^(5)` or `p^(4) q^(5` where
P + q = 9
`(4((p)/(4)) + ((q)/(5)))/(5 + 5) ge [((p)/(5))^(4) ((q)/(5))^(5)]^((1)/(9)`
`implies [((p)/(4))^(4) ((q)/(5))^(5)]^((1)/(9)) le (p + q)/(9)`
`implies ((p)/(4))^(4) ((q)/(5))^(5 le 1`
`implies p^(4) q^(5) le 4^(4) 5^(5)`
Therefore, maximum value of `(7 - x)^(4) (2 + x)^(5)` is `4^(4) 5^(5)`