Question

I haven't really understood this unit at all, can someone help please?

Answer 1

what is it about?

Answer 2

Quadric Functions

Answer 3

sorry can't really help with that :(

Answer 4

That's ok. Thanks though :)

Answer 5

@texaschic101 Hey, do you think you help me?

Answer 6

@mathmale

Answer 7

A) the x-intercept is when f(x) = 0. We know f(x) is the profit, so the x-intercept means he is getting no profit when x=0 and x=4 (and x is the price of notebooks.. so obviously is the price of a pen is 0, he is not making profit, and if the price is 4, he isn't making profit either)... So the price of the notebook is probably too expensive and not enough people are buying it at that price so that he can make a profit.

The function is increasing on \(x \in(−∞,2]\) and decreasing on\( x\in[2,+∞)\) since 2 is the maximum point. Although, you have to realize that realistically, the merchant wouldn't sell notebooks at a cost lower than 0 (that would mean he would be giving away money when people get a notebook).

On the increasing part of the graph: he is continually making more and more profit until he reaches the highest profit attainable at x=2 where his profit is $300.

Then on the decreasing portion of the graph, his profit declines gradually with increasing notebook price (x).

Why isn't he making more money as the price increases all the time (this is relating to the sales of the notebooks)? Well I alluded to that in my first paragraph. There's an economic factor of supply/demand here. On the increasing portion of the graph, people may be fairly "indifferent" about paying for a notebooks for less than 2 dollars, but his max is reached at 2 since it's a higher price. But after 2 dollars, people are less willing to buy notebooks because they are too expensive. And it turns out that not enough people are willing to buy the notebooks at a price greater than 2 for him to make larger profits. This is because you have to realize that there are other costs involved. Like if the merchant buys a box of 3 notebooks, but he only sells 1 of them at a price of 5.75, then he will not make a large profit (of course, depending on the price of the box of notebooks).
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b) Just look where the y-axis cuts at 220$. The curve part above 220 is telling you the part of the graph where the profit is larger than 220. So, the corresponding domain for this is x∈[1,3] (look at the x-axis where the y-value of 220 occurs).
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c) average rate of change... just think of it as a line crossing the points at x=2 and x=4.

The coordinates for these points are (2, 300) and (4, 0). So the average rate of change is
\[\frac{\Delta y}{\Delta x}=\frac{300-0}{2-4}=-150\]
. So the average rate is negative, which means that on average, the profits decrease by $150 per increase in $1 in notebook price.

Answer 8

Oh my gosh, thank you so much!!!

Answer 9

:)