Question

graph the function f(x)=(x+2)(x-4). Which describes all of the values for which the graph is negative and decreasing?

Answer 1

Answer:

$x\in(-2,1)$

Step-by-step explanation:

We are given that a function

$f(x)=(x+2)(x-4)$

$f(x)=x^2-2x-8$

Differentiate w.r.t x

$f'(x)=2x-2$

$f'(x)=0$

$2x-2=0$

$2x=2\implies x=\frac{2}{2}=1$

Therefore, intervals

$(-\infty,1),(1,\infty)$

Interval :$(-\infty,1)$

x=0

$f'(0)=-2$

Decreasing  function.

Interval:$(1,\infty)$

Substitute x=2

$f'(2)=2(2)-2=2>0$

Function increasing.

From given graph we can see that function is negative for the values of x

-2<x<4

Hence, the graph is negative and decreasing for the values of x

$x\in(-2,1)$