Question

FAN AND MEDAL

The graph below shows a company's profit f(x), in dollars, depending on the price of pencils 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? (5 points)

Part B: If at one time the profit of the company was at least $100, what domain could possibly produce this profit? (2 points)

Part C: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what doe

Answer 1

@math&ing001 can you help me please

Answer 2

Yeah sure. The x-intercept represent when the company's profit equals 0. The max value represents the max profit.

Answer 3

The graph shows that when the price of the pencil is below 5 the company's profit decreases (function is decreasing).
Similarly, when the price of the pencil is above 5 the company's profit increases (function is increasing).

Answer 4

ok

Answer 5

how do i find the intervals?

Answer 6

This should help you for part B :

Answer 7

ok um so the domain would be between 2 and 8 right

Answer 8

Correct !

Answer 9

so the domain would be at 5

Answer 10

(5,100) to be precise right

Answer 11

No, the domain is what you said earlier [2,8]. Why would it be 5 ?

Answer 12

oh ok i got mixed up sorry

Answer 13

No worries, here's a hint for part C :

Answer 14

so the average rate of change is 60 and the domain is (2,5)

Answer 15

is that correct?

Answer 16

Average rate of change formula is : \(\frac{ f(x2)-f(x1) }{ x2 - x1 }\)

Answer 17

Here you have x2=5 and x1=2

Answer 18

ok

Answer 19

so f(5)-f(2)
_________ correct
5-2

Answer 20

Yep ! Keep going =)
Replace f(5) and f(2) with their values.

Answer 21

so 160 - 100
---------
5-2

Answer 22

Yes, and that would equal ?

Answer 23

f subtracted the it would be 60/3

Answer 24

Ok, now divide 60/3 :)

Answer 25

so 20?

Answer 26

Yep correct !

Answer 27

oh ok thank you so much sir for the help so the domain would be (2,5) right also one more thing how do i find the intervals for A i think i have an idea how but im not 100% sure

Answer 28

I don't see a question about the domain, maybe you could finish this :
"Part C: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what doe..."
For the intervals:
]-infinity, 5] f(x) increases.
[5, +infinity[ f(x) decreases.

Answer 29

o ok thank you so much sir you have been a great help

Answer 30

You're welcome !