Question

You are having a meeting with the CEO of a technology company. You have interpreted the number of laptops produced versus profit as the function P(x) = x4 − 3x3 − 8x2 + 12x + 16. 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)

Answer 1

P(x) = x^4 - 3x^3 - 8x^2 + 12x + 16

breakeven ocuurs when P(x) = 0

so, finding the zeros of the function

x^4 - 3x^3 - 8x^2 + 12x + 16 = 0

the polynomial has possible rational roots at

x = +- { 1 , 2 , 4 , 8 , 16 }

now testing each root one by one

we find that actual root are

x = -1 , 2 , -2 , 4

so, company break even occurs when 1 laptop or 4 laptops are produced

the graph will have 2 minimums and 1 maximum

the graph will start off decreasing and and end off increasing

the profit starts to increase when they produce more than 4 laptops