Question

You are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function P(x) = x4 + 2x3 + 6x2 - 3x - 7. 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

Help with give medal!

Answer 2

looks like this
ww.wolframalpha.com/input/?i=x4+%2B+2x3+%2B+6x2+-+3x+-+7

Answer 3

It won't open @misty1212

Answer 4

A letter "w" was missing at the beginning to make www.
Try this:
www.wolframalpha.com/input/?i=x4+%2B+2x3+%2B+6x2+-+3x+-+7

Answer 5

Thanks for the website but i still dont understand how to answer the question

Answer 6

can you help or not? @mathmate

Answer 7

We'll look at the questions one by one.
a. Describe to the CEO what the graph looks like. Use complete sentences, and
b. focus on the end behaviors of the graph
c. and where the company will break even (where P(x) = 0)
Can you answer (a), post your attempt please.

Answer 8

The graph at first will appear negative then it will it will increase becoming positive. The graph will appear in a U shape. The function is positive therefore opens upward. End behavior of the function at the left and right ends of the graph. The distance between the curve and the line approaches zero as we move out further and further out on the line. The company will P(x)=0 when its at (0,-7).

Answer 9

Pretty good attempt.
The statement "at first negative" is misleading if we do not specify the domain, which is [0,+inf).
Also, it does not immediately increase. It decreases until approx. 0.25 to about -0.73 where there is a local minimum. Subsequently it increases.
BTW, calculus can be used to find a lot of the information, if you have already done differential calculus.

Answer 10

* until x=0.25 where y=-0.73 approx.

Answer 11

thank you. is the rest of my answer correct or no?

Answer 12

You can find the local minimum and where it occurs using calculus.
Also with concavity, it's upwards throughout, by verifying f"(x) for all x>=0.
The sign of the function is the answer to part C.

I do not see that you have explicitly answered part (b) about end behaviours, although saying that it has a U-shape implicitly answers the question.
Much of the time, knowing the definition of terms will give you an answer to the point.
Here's some info. on end-behaviour:
http://www.purplemath.com/modules/polyends.htm

Break even point is the value of x (sales) is when P(x)=0.

Answer 13

Break even point is the sales volume when profit equals zero (i.e. not P(0))

Answer 14

Okay thank you so much

Answer 15

You're welcome! :)