Question

What is the sign of f on the interval -2

Answer 1

Answer:

$f$ is sometimes positive and sometimes negative.

Step-by-step explanation:

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

Take $x=-1\in(-2,\frac{9}{2})\ as-2$

$f(-1)=(-1-3)(-1+2)(-1+4)(-1-1)(-2-9)\\\\=(-4)(1)(3)(-2)(-11)\\\\=-264\\\\f(-1)$

Take $x=2\in(-2,\frac{9}{2})\ as\ -2$

$f(2)=(2,-3)(2+2)(2+4)(2-1)(2\times2-9)\\\\=(-1)(4)(6)(1)(-5)\\\\=120\\\\f(2)>0$

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

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