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)=-x^4+x^3+7x^2-x-6. Describe to the CEO what the graph looks like. Use complete sentences & focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

Answer 1

The graph has domain x ∈ ( 0 , +∞ )
It is first increasing and then decreasing. It has a local minimum and a global maximum.
- x^4 + x³ + 7 x² - x - 6 = ( x - 1 ) ( x + 1 ) ( x + 2 ) ( 3 - x )
The company will break even when P ( x ) = 0
The zeroes are:  x 1 = 1,  x 2 = 3
The company has a profit when:  x  ∈ ( 1, 3 )