The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, being sold by the company:
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (6 points)
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?

- anonymous

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@Needhelpp101

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@e.mccormick can you help?

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@Algorithmic

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Show an attempt at your question, or at least write out what exactly you do not understand. Do you know what the \(\it x\)-intercepts are?

- anonymous

ok. i think that the maximum value represents the maximum amout of pens the sell? i really dont know how to do this kind of math

- anonymous

@Algorithmic

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hello?

- anonymous

We are told that the graph shows a company's profit \(f(x)\), in dollars, depending on the price of pens \(x\), in dollars, being sold by the company. In this case \(f(x)\) is the \(y\)-axis.
Part A: What do the x-intercepts and maximum value of the graph represent?
The \(x\)-intercepts are where the graphs intersects the \(x\)-axis. On your graph that would be in two places. So what do the \(x\)-intercepts represent according to the question? Well if the price of pens is the \(x\)-axis, and the \(y\)-axis is the profit of the company tied to the price of the pens, then if the pens are priced at zero the company makes no profit. (Do you understand how I derived that?)

- anonymous

i think so

- anonymous

Okay, so what would the maximum value of the graph represent, if the \(x\)-intercepts represent the company making no profit.

- anonymous

0

- anonymous

Erm, how did you get that? The maximum value of the graph would represent the maximum profit.

- anonymous

oh okay 120?

- anonymous

Erm, the are not asking for a distinct value, rather they are asking for what it represents.

- anonymous

I dont know, their profits?

- anonymous

Well, yeah in a way. However as I said above, the maximum value, represents the maximum profit they made. That is all there is to answer that question.

- anonymous

OOHH okay thanks for that!

- anonymous

Okay, so have you tried to attempt the question:
What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

- anonymous

is it 3,120? i think it represents that they've only sold 3 so far, and thats the maximum that they've made @Algorithmic

- anonymous

what do you think?

- anonymous

@Needhelpp101

- anonymous

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