`f(x)=(x-8)^4(x-9)^5,0lt=xlt=10 ,` monotonically decreases in (a) `(76/9, 10]` (b) `(8, 76/9)` (c) `(0,8)` (d) `((76)/9, 10)`

Options

A. `((76)/(9),10)`
B. `((8),(76)/(9))`
C. [0,8)
D. `((76)/(9),10)`

Answer

2

Explanation

`f(x)=(x-8)^(4)(x-9)^(5),0lexle10`
`therefore f(x)=4(x-8)^(3)(x-9)^(5)+5(x-9)6(4)(x-8)^(4)`
`=(x-8)^(3)(x-9)^(4)[4(x-9)+5(x-8)]`
`=9(x-8)^(3)(x-9)^(4)(x-(76)/(9))`
singn scheme of f(X) is as follows
`f(X) lt 0 if x in (8,(76)/(9))` i.e f(X) decreases if x in `8,(76)/(9)`