## anonymous one year ago Please help! The graph below shows a company's profit f(x), in dollars, depending on the price of notebooks 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? Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit? Part C: What is an approximate average rate of change of the graph from x = 2 to x = 4, and what does this rate represent? • This Question is Closed 1. anonymous 2. anonymous @Thesn1 can you please help I tried googling it and I cant find it 3. anonymous @jim_thompson5910 hey can you help? 4. jim_thompson5910 how far did you get with this? did you get started at all? 5. anonymous you want solution of all this or just the last question ?? 6. anonymous @jim_thompson5910 no I didn't start im confused with this topic 7. jim_thompson5910 what does x represent (this is given at the top) ? 8. anonymous x is price of notebooks 9. jim_thompson5910 how about f(x) ? 10. anonymous company's profit 11. jim_thompson5910 correct 12. jim_thompson5910 the x-intercepts are when f(x) = 0 so what does f(x) = 0 mean? 13. anonymous that the company started at$0?

14. jim_thompson5910

not really "started" but just whenever the profit is $0 since f(x) = profit 15. anonymous oh ok. so for part a the x intercepts are 0 and 4 right? 16. jim_thompson5910 correct, so what does that mean? 17. anonymous ummmmmm. idk? 18. jim_thompson5910 when x = 0, the value of f(x) = 0 so when the price is$0, the profit is $0, agreed? 19. anonymous ya agree. so What do the x-intercepts and maximum value of the graph represent? 20. jim_thompson5910 what does the x intercept of 4 represent? 21. anonymous the profit is$4?

22. jim_thompson5910

not quite

23. anonymous

then idk. im not good at quadratics

24. jim_thompson5910

when the price is $4, the profit is$0

25. anonymous

oh ok. so the x-intercepts are 0 and 4, and maximum value of the graph represent what?

26. jim_thompson5910

when they say "max value" they mean the max value of f(x) how big can f(x) get?

27. anonymous

300.

28. jim_thompson5910

yep so that is the max profit because again, f(x) is the profit

29. jim_thompson5910

what value of x corresponds to the max profit?

30. anonymous

ok and 2.

31. jim_thompson5910

yep so when x = 2, f(x) = 300 therefore, when the price is $2, the max profit is$300. This is where the company wants to aim

32. anonymous

ok that makes more sense. ok and then for part a still What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

33. jim_thompson5910

the function is increasing if you are going uphill as you go from left to right decreasing is the opposite way (downhill) as you go from left to right

34. jim_thompson5910

|dw:1433120212372:dw|

35. jim_thompson5910

|dw:1433120219258:dw|

36. jim_thompson5910

|dw:1433120232720:dw|

37. anonymous

ok so what would I put for part a answer?

38. jim_thompson5910

for the increasing/decreasing part, they just want the intervals along the x axis

39. jim_thompson5910

for example (this is not the answer, just an example) say we had this scale |dw:1433120434137:dw| the increasing interval would be from x = 0 to x = 10 you can write that as 0 < x < 10 or in interval notation as (0,10) the decreasing interval would be from x = 10 to x = 20 you can write that as 10 < x < 20 or in interval notation as (10,20)

40. anonymous

i don't get it. @jim_thompson5910

41. jim_thompson5910

where are you stuck at

42. anonymous

i just don't understand what you just said for the intervals.

43. jim_thompson5910

do you see how on my example graph, the curve goes uphill as you go from left to right until you hit x = 10?

44. anonymous

ya

45. jim_thompson5910

so that's how I got the interval from 0 to 10 0 < x < 10 basically when x is between 0 and 10, the graph is going uphill...ie increasing

46. anonymous

oh ok so for my graph, it would be 0<x<300 right?

47. anonymous

for increasing. and then i don't know about decreasing

48. jim_thompson5910

actually 0 < x < 2 look along the x axis (not y)

49. anonymous

ohhhhhh. so what would the decreasing be?

50. jim_thompson5910

give it a shot

51. jim_thompson5910

hopefully you see how I'm getting 0 < x < 2 ?

52. anonymous

2<x<50?

53. jim_thompson5910

that's a possibility, but to be really practical, the company only cares about when the profit is 0 or positive (ideally when it's positive) so it would be from x = 2 to x = 4. Anything beyond x = 4 is territory the company doesn't want to go into so that's why it's practical to say 2 < x < 4 is the interval in which the function is decreasing. In a practical context anyway

54. jim_thompson5910

notice how with the increasing part, I ignored everything to the left of x = 0

55. anonymous

ya. ok so i just have to look at the x axis right? when i do this

56. jim_thompson5910

yeah whenever looking at intervals of decreasing or increasing

57. anonymous

ok got it! thanks i do flvs and its hard to do algebra online. anyways, to answer the whole part of part a, how would i put it as

58. jim_thompson5910

Simply state in your own words the things we went over the roots, the max, the increasing/decreasing intervals

59. anonymous

but itt also says what does it represent and idk what to put for that

60. anonymous

Part B: At one time the profit of the company was at least $220, what domain could possibly produce this profit? @jim_thompson5910 61. anonymous @jim_thompson5910 can you help me with part b and c!!?? 62. jim_thompson5910 draw a horizontal line through y = 220 where does this horizontal line cross the parabola? at what two points? 63. anonymous how do i do that? 64. jim_thompson5910 65. anonymous ok so (1,220) and (3,220) 66. jim_thompson5910 yes 67. jim_thompson5910 so the profit is at least$220 when x is between 1 and 3 (inclusive) $\Large 1 \le x \le 3$

68. jim_thompson5910

if the company wants a profit of $220 or greater, then it needs to have the price between$1 and $3 69. anonymous ok so that would be my answer? 70. jim_thompson5910 yeah the domain is another way of asking for an interval 71. jim_thompson5910 do you see how to do part C? 72. anonymous um no i need help with this sorry 73. jim_thompson5910 what are the two points on the parabola when x = 2 and x = 4? 74. anonymous x= 2 is 300? and x=4 0? 75. jim_thompson5910 yep so we have the two points (2,300) and (4,0) 76. jim_thompson5910 what is the slope of the line through those two points? 77. anonymous would it be a decreasing line 78. jim_thompson5910 yes the slope is some negative number 79. anonymous ok so what would my answer be, A negative line that goes through 2,300 and 4,0 80. jim_thompson5910 use the slope formula $\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ 81. jim_thompson5910 what slope do you get? 82. anonymous um one second let me solve it 83. anonymous -150 84. jim_thompson5910 correct 85. jim_thompson5910 so the average rate of change from x = 2 to x = 4 is -150 what does this mean? it means that the profit decreased by an average of$150 per increase of the price by $1 (ie each time the price went up$1, the profit dropped by \$150)

86. anonymous

ok so -150 is the approximate average rate of change. and this rate represents what? so i put that down?

87. jim_thompson5910

yeah in your own words of course

88. anonymous

ya ik that. thanks so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

89. jim_thompson5910

you're welcome