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).

Question

Mathematics

Callum Hernandez

23 March, 20:53

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).

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August · 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)