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anonymous

  • one year ago

Pretty lost on this problem! Help needed! Q: Suppose that 3 less than or equal to f^(x) is less than or equal to 5 for all values of x? Show that 18 is less than or equal to f(8)- f(2) is less than or equal to 30.

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  1. anonymous
    • one year ago
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    I dont really know where to start..

  2. dan815
    • one year ago
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    Show that 18 is less than or equal to f(8)- f(2) is less than or equal to 30. what is thsi part saying

  3. anonymous
    • one year ago
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    Here lemme right it out: Suppose that \[3\le f'x \le 5 \]

  4. dan815
    • one year ago
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    oh xD thats a derivative haha

  5. anonymous
    • one year ago
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    and show that \[18 \le f(8) - f(12) \le 30 \]

  6. dan815
    • one year ago
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    okk

  7. anonymous
    • one year ago
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    lol yea

  8. dan815
    • one year ago
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    basically, lets consider the max slope and min slope

  9. dan815
    • one year ago
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    f'(x) has a min of 3 and max of 5 slope, what can we say about the distance change from f(8) to f(12) then

  10. dan815
    • one year ago
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    i see you wrote f(2) up in your question then f(12) rewritten which one is it exactly?

  11. anonymous
    • one year ago
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    its f(2), sorry about that

  12. dan815
    • one year ago
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    okay so

  13. dan815
    • one year ago
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    do you have any ideas so far?

  14. anonymous
    • one year ago
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    how would you solve for what f(8) and f(2) is if they dont even give you what the orignal function is?

  15. dan815
    • one year ago
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    we dont know f(8) and f(2) but we can see the max and min difference

  16. dan815
    • one year ago
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    |dw:1437625240205:dw|

  17. dan815
    • one year ago
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    lets the slope function is some arbitrary function like this that si contained in slope 3 to 5

  18. dan815
    • one year ago
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    you can say the max change will be if its slope 5 everywhere and hte min change will be if the slope is 3 everywhere

  19. anonymous
    • one year ago
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    yea thats given from the first info

  20. dan815
    • one year ago
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    so you see f(8)-f(2) if f'(X) WAS 5 EVERYWHERE and then f(8)-f(2) if f'(x) was 3 everywhere

  21. dan815
    • one year ago
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    does this make sense?

  22. anonymous
    • one year ago
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    yea, thanks for capitalizing it

  23. dan815
    • one year ago
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    lol

  24. dan815
    • one year ago
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    does it really make sense?

  25. anonymous
    • one year ago
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    NO. I dont even get what this question is asking honestly... im super confused.

  26. dan815
    • one year ago
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    ok ok lets start over

  27. anonymous
    • one year ago
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    I need to go back to square 1 or something

  28. dan815
    • one year ago
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    dont worry

  29. dan815
    • one year ago
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    okay f'(x) the first derivatve of x means its giving u the slope of your function everywhere

  30. anonymous
    • one year ago
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    yes, I get that

  31. dan815
    • one year ago
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    okay now, they tell you the slope isalways somewhere in between 3 and 5

  32. anonymous
    • one year ago
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    Yes, so we assumed 3 is the min slope and 5 is the max slope

  33. dan815
    • one year ago
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    now our job is to find the most change possible and the least change possible for our function f(x) given this info

  34. dan815
    • one year ago
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    we can say the most change happens when the slope is always at 5 and the least change when the slope is always at 3

  35. dan815
    • one year ago
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    now a constnat slope means the function is a line so to find the max and min changes we have to look at lines here

  36. dan815
    • one year ago
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    |dw:1437625618806:dw|

  37. dan815
    • one year ago
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    i dont know what f(8) and f(2) are but since the slope is constant i do know the changge in height

  38. anonymous
    • one year ago
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    love the drawing, its makes more sense to me that way

  39. dan815
    • one year ago
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    |dw:1437625668687:dw|

  40. dan815
    • one year ago
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    |dw:1437625704207:dw|

  41. anonymous
    • one year ago
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    wait, how were you able to assume that you could draw the right triangles like that in the diagram?

  42. dan815
    • one year ago
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    that just me finding the change of height for a line with slope 5

  43. dan815
    • one year ago
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    since its f(8)-f(2) the change in x was 8-2 and to find the change in y i know the slope of the line is 5, and slope = rise/run so 5 slope means for every run there is 5 rise so 8-2=6 rrun so for 6 run there is 6*5 rise

  44. dan815
    • one year ago
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    and the reason its right angle triangle is because run is horizontal and rise is vertical horizontal and vertical lines have a 90 degree angle

  45. anonymous
    • one year ago
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    OMG that was so easy!!!!

  46. dan815
    • one year ago
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    lol xD

  47. dan815
    • one year ago
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    im glad u find htis easy now

  48. anonymous
    • one year ago
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    . Oops

  49. anonymous
    • one year ago
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    Meant to say thanks! Appreciate the help! :)

  50. dan815
    • one year ago
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    no its good,. its supposed tofeel easy once your understand it

  51. dan815
    • one year ago
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    you already thanked me by saying omg its so easy

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