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. Use complete sentences and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

Question

anonymous · Answer

so far i said this:

The degree is even so the ends on the graph will travel in the same direction. The the ends will both continue up because the leading coefficient is positive.

anonymous · Answer

i also have this question;

Two students in your class, Hunter and Maggie, are disputing a function. Hunter says that for the function, between x = -2 and x = 2, the average rate of change is 0. Maggie says that for the function, between x = -2 and x = 2, the graph goes up through a turning point, and then back down. Explain how Hunter and Maggie can both be correct, using complete sentences.

jdoe0001 · Answer

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jdoe0001 · Answer

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anonymous · Answer

im not sure i understand your picture

jdoe0001 · Answer

well, do you know what a rate of change is?

anonymous · Answer

yes, its the slope

jdoe0001 · Answer

so if between -2 and 2, the slope goes equally UP as well as DOWN, it will cancel out and thus give a total rate of change of 0 for the interval of [ -2, 2 ]

anonymous · Answer

that makes sense, thank you! and would you happen to know my other question as well?

jdoe0001 · Answer

your end behaviour sentence looks good, the graph goes Up Up Up to $+\infty$

anonymous · Answer

so does that explain why it breaks even?

jdoe0001 · Answer

hmmm it doesn't .... hmmm

anonymous · Answer

do you know how i would explain it to why it breaks even then?

jdoe0001 · Answer

well... it'd be at P(x) = 0.. that is $\bf 0= x^4 −3x^3 −8x^2 + 12x + 16$    so that means the x-intercepts
when y = 0, or profits are non-existent, for the amount of produced laptops
so, you make so many laptops, they yield a revenue that only covers the costs of producing them, but no profits, at the x-intercepts

jdoe0001 · Answer

there should only be one break-even point.... so I'd think it be the x-intercept before the graph takes off up up up, from that x-intercept, 0 profit or y = 0, the more laptops produced will yield a profit that's ever increasing

anonymous · Answer

okay thank you so much for your help!!!

jdoe0001 · Answer

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