Question

What is the sign of f on the interval -2

Answer 1

`f` is sometimes positive and sometimes negative.

Explanation:

`f(x)=(x-3)(x+2)(x+4)(x+4)(x-1)(2x-9)`

Take
`x=-1\in(-2,(9)/(2))\ as-2<-1<(9)/(2)`

`f(-1)=(-1-3)(-1+2)(-1+4)(-1-1)(-2-9)\\\\=(-4)(1)(3)(-2)(-11)\\\\=-264\\\\f(-1)<0`

Take
`x=2\in(-2,(9)/(2))\ as\ -2<2<(9)/(2)`

`f(2)=(2,-3)(2+2)(2+4)(2-1)(2*2-9)\\\\=(-1)(4)(6)(1)(-5)\\\\=120\\\\f(2)>0`

Hence
`f(x)<0` for
`x=-1` and
`f(x)>0` for
`x=2`

So
`f` is sometimes positive and sometimes negative in the interval.