A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Still confused...so sorry...am not sure how to differentiate to find points where d(area)/dx has maxima. Yet another weakness..please help Suppose that 320 feet of fencing are available to enclose a rectangular field and that one side of the field must be given double fencing. What are the dimensions of the field of maximum area?

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what do you understand about the derivative of a function?

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Not much to be honest..I am really not doing so well with algebra...it's tough

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats fine, I can work with that :)

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know what slope is? like if you look at a roof, how steep the roof is is determined by its slope right?

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okayu

  6. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the derivative of a funtion tells us the slope at any given point. So we can see how steep it is. does that make sense?

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i just did slopes..i didn't do so great, but at least got a C that week ..I do understand the idea of it i supposee

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, that makes sense..

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    My pc is running a tad slow..

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    can you tell me which one of the green lines has a "0" slope? in other wirds, it is perfectly flat?

    1 Attachment
  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I was under the assumption that both sides are part of the slope; however the one on the right seeems straight

  12. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is the one on the right flat? we are looking for the line that is straight across fromleft to right with no slope; like a flay desert

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    flat desert

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Are you referring to the x-axis

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    here is another example; the places where the green lines are flat across the screen from left to right; are where there is "0" slope. Does that make sense?

    1 Attachment
  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh, wow...yes, I see it...sorry, must be blind..I assumed it was just the x-axis. Okay, on the same page

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Makes sense yes..thank you for being patient

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ;)

  19. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so the derivative of an equation tells us the "slope" at any gien point; can you see that when the slope = 0 that we have a high spot or a low spot in the graph?

  20. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    at any "given" point.... typos persist lol

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I believe so...

  22. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when the derivative of an equation is equal to 0; we have 3 possible conditions. The point is a MAX The point is a MIN or the point is giving us a false reading and is an inflection point between concavities...

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, that maeks sense

  24. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good :) Now lets see how it applys to your problem with the fencing :)

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay

  26. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Suppose that 320 feet of fencing are available to enclose a rectangular field and that one side of the field must be given double fencing. What are the dimensions of the field of maximum area? We have a total of 320 feet of fencing; and we know that one side is double fenced. We also know that it is a rectangle: Like this:

    1 Attachment
  27. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x + 2x + y + y = 320 feet around the outside right? and the Area of the rectangle is: A = xy lets use these to our benefit.

  28. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3x + 2y = 320 y = (320-3x)/3 is what we get for a "value" of y right? Lets use this "y" value in our Area equation

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, got you so far

  30. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    A = x(320-3x)/3 A = (320x)/3 -(3x^2)/3 Now we can use rules of derivatives to find the derivative of A with respect to x. Okay?

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay....im hanging in there

  32. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The Power rule for derivatives states: Dx(Cx^n) = Cn x^(n-1) A' = 320/3 -6x/3 = 320/3 - 2x When 320/3 - 2x = 0, we have either a MAX or a MIN condition :)

  33. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    320/3 - 2x = 0 ; multiply by 3 320 - 6x = 0 ; subtract 320 -6x = -320 ; divide by -6 x = 320/6 = 53' 2/6 = 53' 1/3 feet; lets see if this works in our problem :) And if you have any questions on it let me know...

  34. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wow.,,.rough

  35. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3x + 2y = 320 ; x = 320/6 for simplicities sake :) 3(320/6) + 2y = 320 320/2 + 2y = 320 2y = 320-320/2 y = (320/2)/2 y = 320/4 = 80. double check: 3(320/6) + 2(80) = 320 320/2 + 160 = 320 320/2 + 320/2 = 640/2 = 320 :) So whats our Area then... A = x(y) A = 320(80)/6 A = 4266' 2/3 feet

  36. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    squared feet lol

  37. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wow...You know your stuff. I can use this to help me with the others. I really appreciate you taking the time to explain this to me.

  38. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The key is to find out what x and y are in terms of one variable: We found that y = (320-3x)/2 right? Then we used that "value" in the Area formula of a rectangle to determine its equation in terms of just the x variable. A = 320x/3 - x^2 We then take the derivative to find a slope of "0" The value of "x" that we find in the derivative is the MAX condition for x; Use that value to determine the your real "y" value :) then compute the area for xy ;)

  39. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Youre welcome :) I hope it helps

  40. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The procedure was good, but I see a spot where I messed up the math :)

  41. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y = (320-3x)/2 ; I wrote /3 in the rest and messed up the numbers lol

  42. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol...

  43. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, should I replug in the numbers then?

  44. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y = (320-3x)/2 A = x(320-3x)/2 A = 160x -(3/2)x^2 A' = 160 - 3x = 0 x = 160/3 ................... 3x +2y = 320 3(160/3) + 2y = 320 160 + 2y = 320 2y = 160 y = 80 ........................... x = 160/3 ; y = 80 Area = 160(80)/3 Area = 4266' 2/3 I got different number for x bu tthe same values lol....

  45. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that worked out pretty lucky; 320/6 actually reduces to 160/3..... dont ask me how that worked in my favor lol

  46. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I see what I did; I transposed the x and y; got the resulting values which would have been the same regardless; and produced identical results... Im a genius lol

  47. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So, shall I keep the original information to use?

  48. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the original is good; I actually used the transposed numbers the second time. So use work the first time as the answer if you wanna get a taste for what I did; if you wanna see how my stupidity plays in my favor for the second attempt, by all means, parse thru that one as well ;)

  49. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Wow, too funny.

  50. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you think you could help me out with something else since you are so good at explanation?

  51. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I can, but please post a new question for it :)

  52. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh, okay, I can do that...

  53. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.