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) = x^4 -3x^3 -8x^2 + 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).

Answer 1

@ganeshie8

Answer 2

did you graph the function, you need a graphing calculator

Answer 3

or we can use an online calculator

Answer 4

copy and paste your function x^4 -3x^3 -8x^2 + 12x + 16
into
https://www.desmos.com/calculator

put it in box 1

Answer 5

ok i did, what now ?

Answer 6

it opens upward

Answer 7

now find where P(x) =0, that is , find the x intercepts

Answer 8

you can point and click on the x intercept

Answer 9

x = 2 and x =4 ?

Answer 10

right

Answer 11

I don't think the first x intercept makes sense for this problem

Answer 12

because at first you should have negative profit, when you start to produce units (widgets, calculators, laptops, etc)

Answer 13

well it shows x = -2 , x = -1, x = 2, and x = 4

Answer 14

right, x = -1 and x = -2 does not make sense for the problem

Answer 15

You can make a profit from one laptop. You break even with two laptops. You take a loss with three laptops. You break even again with four laptops. With five laptops and more, your profit continues to rise as the number of laptops increases.

Answer 16

Ok so I could say the graph opens upward(means it's positive?), and the company breaks even at 4 laptops. what else would i say or is that it?

Answer 17

that it continues on to infinity?

Answer 18

@perl

Answer 19

yes

Answer 20

5 laptops and more is profit (to infinity) , obviously this is not realistic, its just a projection , all else being equal (if everything stays the same)

Answer 21

thank you :)