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 and, in general, how to sketch the graph without using technology. use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where p(x) = 0). (10 points)

Given Function is,

Which is the bi quadratic function.

For x-intercept, P(x)=0

Thus,

⇒

⇒

⇒ The x-intercept of the functions are, (-2,0),  (-1,0), (1,0) and ( 3,0)

Similarly, for y-intercept,

x = 0 , y = -6

Thus, y-intercept of the given function is,  (0,-6)

The critical points of the function f(x) are ( where f'(x) = 0), (2.254, 12.949)

and (-1.574, 2.879)

End Behavior:

Since, The leading coefficient is negative and has even degree,

Therefore, end behavior of the given function is,

as

And, as

it happens during combustion and impacts the environment because the plants and trees take in that and it can cause them to die.