Question

NEED HELP!!! WILL MEDAL!!!

Answer 1

The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, being sold by the company:

Answer 2

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?

Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?

Answer 3

where do you think the maximum profit is?

Answer 4

idek man i'm way confused

Answer 5

what do you think? take an educated guess

Answer 6

Dude when i say idk i really do mean it. I have no clue how to answer this. I have no educated guess because i'm not very educated in this

Answer 7

f(x) or y = profit while x is the price

Answer 8

ok

Answer 9

there's a minimum price that gives a maximum profit you move a way from this price the profit goes down in both directions.

Answer 10

alright

Answer 11

now look for the maximum value on the graph

Answer 12

270?

Answer 13

now what price is associated with that? and what does 270 represent?

Answer 14

profit?

Answer 15

yes

Answer 16

Max. profit. This occurs at what price? Read this off the x-axis.

Answer 17

1-8?

Answer 18

now, let's look at the x intercepts

Answer 19

ok

Answer 20

x intercept is when y = 0 or in other words that's when profit is what?

Answer 21

huh? sorry i didn't understand that

Answer 22

yeah so take a look at when x = 0, and 8

Answer 23

x =0 and x = 8 do we have profit?

Answer 24

no?

Answer 25

yes that's correct because y = 0 at these points. x = 8 we can assume that at x = 8 the erasers are too expensive and on one is going to buy them; also at x = 0 well that's relatively easy to conclude why there isn't any profit.

Answer 26

alrighty :D

Answer 27

You understand that?

Answer 28

yep! would that be Part A?

Answer 29

yes

Answer 30

ok now Part B

Answer 31

\[\frac{ \Delta~y }{ \Delta~x } = Average~rate~of~change \]

Answer 32

x = 1 and x = 4 :

Answer 33

find the y point at x = 1 and the y point at x = 4 and find the slope.

Answer 34

x=120 x=270

Answer 35

slope is y=mx+b right?

Answer 36

we just need m

Answer 37

y2-y1/x2-x1

Answer 38

\[\frac{ 270-120 }{ 1-4 } = ? \]

Answer 39

50/3

Answer 40

?

Answer 41

no

Answer 42

150/3

Answer 43

=50

Answer 44

yep, so what this means is that as the price increases from 1 to four dollars

Answer 45

the profit is increasing by an average of 50 dollars

Answer 46

so it represents profit increase?

Answer 47

let's not just focus on a yes or no but do you understand why though? can you tell me why this is the case? this will make things clearer

Answer 48

what's happening from x =1 to x = 4 on our graph?

Answer 49

the profit increases 50

Answer 50

wait can we go back to Part A where it talks about "What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?"

Answer 51

you still there?

Answer 52

yeah so immediately we know in that interval from 1-4 the profit is increasing

Answer 53

what about from x = 4, x = 8 what's happening to the profit.

Answer 54

It's decreasing

Answer 55

why might you think so?

Answer 56

the line parabola is going down

Answer 57

am I wrong?

Answer 58

no you're not. I was asking that because if you notice, the price is getting more expensive so the profit is going down.

Answer 59

ohh ok

Answer 60

so like one reason is possibly that as the price goes up, it's becoming more expensive. right at 4 dollars the profit is the highest then if you make it either more or less expensive to 4 profit goes down.

Answer 61

I'm pretty sure I got it now.

Answer 62

nice

Answer 63

Thank you so much for your help. also thank you for being so patient with me

Answer 64

yeah no problem anytime