Question

You are having a conference call with the CEO of a paper company. You have interpreted the number of trees cut down versus profit as the function P(x) = -x4 + x3 + 7x2 - x - 6. Describe to the CEO what the graph looks like. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).
help pleaseeee!!!

Answer 1

@mathmale

Answer 2

@SolomonZelman

Answer 3

@undeadknight26

Answer 4

Okay, so the graph of P(x) would be, this
https://www.desmos.com/calculator/dsk5edlkpy

And seeming, when x→ ±∞ then y→ -∞ (whether x → ∞ or x→ - ∞ )

Answer 5

p(x)=0, you will need to set \(\normalsize\color{blue}{ P(x)=-x^4+x^3+7x^2-x-6}\)
\(\normalsize\color{blue}{ 0=-x^4+x^3+7x^2-x-6}\)
and sovle for x.

Answer 6

and how would you solve for x in the problem?

Answer 7

I will give you a hint:
\(\normalsize\color{blue}{ -x^4+x^3+7x^2-x-6=-(x-1)(x+1)(x+2)(x+3)}\)

Answer 8

So,

\(\normalsize\color{blue}{-x^4+x^3+7x^2-x-6=0}\)
\(\normalsize\color{blue}{-(x-1)(x+1)(x+2)(x+3)=0}\)
\(\normalsize\color{blue}{(x-1)(x+1)(x+2)(x+3)=0}\)

the roots are ?

Answer 9

roots, x-intercepts, same thing ;)

Answer 10

arent they 1,2,3,6 ?

Answer 11

\(\normalsize\color{blue}{(x-1)(x+1)(x+2)(x+3)=0}\)
\(\huge\color{blue}{~↓~↓~~↓~↓ }\)

1 -1 -2 -3

Answer 12

Makes sense ?

Answer 13

okay so the roots are 1,-1 ,-2,-3?

Answer 14

yes

Answer 15

so what do i do next

Answer 16

are you still there ? @SolomonZelman