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).
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 )
