30 POINTS!!!!!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).

Since we have a negative 4th degree function, the graph will start off increasing, and then end off decreasing. This is a symmetrical function. Using this fact, we know can tell the shape the graph. It will have 2 maximums and 1 minimum. There is a maximum in the interval (-2, -1), a minimum in the interval (-1, 1), and another maximum in the interval (1, 3). This is in the general sense of the graph.

However, the number of trees must be positive. So the company makes a minimum profit when they don't cut down any trees. The company makes a maximum profit when 2 trees are cut down. When no trees are cut down, the company loses profit by 6.

As for the end behaviors, x cannot be negative because you cannot cut down negative number of trees. Therefore, the graph starts at x=0.