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:the answer is c/ all real values of x where 1<x<4

Explanation:

edge 2020

Answer 2

`x\in(-2,1)`

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=(2)/(2)=1`

Therefore, intervals

`(-\infty,1),(1,\infty)`

Interval :
`(-\infty,1)`

x=0

`f'(0)=-2<0`

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)`