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lilly21 Group Title

locate the absolute extrema of the function (if any exist) over the interval. f(x)=2x-3 [0, 2]

  • 2 years ago
  • 2 years ago

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  1. infoshark Group Title
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    Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?

    • 2 years ago
  2. lilly21 Group Title
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    2

    • 2 years ago
  3. infoshark Group Title
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    what are the roots of 2 ? where does it cross the x axis

    • 2 years ago
  4. lilly21 Group Title
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    at y=0???

    • 2 years ago
  5. infoshark Group Title
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    can y ever be zero if it always equals 2 ?

    • 2 years ago
  6. lilly21 Group Title
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    nope

    • 2 years ago
  7. infoshark Group Title
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    any max extrema then ?

    • 2 years ago
  8. infoshark Group Title
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    abs*

    • 2 years ago
  9. lilly21 Group Title
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    im kinda of confused by ur question :[

    • 2 years ago
  10. hartnn Group Title
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    u got x=2 put it in f(x) to find the extrema

    • 2 years ago
  11. lilly21 Group Title
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    1 ?

    • 2 years ago
  12. hartnn Group Title
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    thats correct :)

    • 2 years ago
  13. lilly21 Group Title
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    thats it?

    • 2 years ago
  14. hartnn Group Title
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    wait. for extrema, u take derivative and equate it to 0 means you do, f'(x)=0 but you got f'(x) = 2 hence there is no extrema.....

    • 2 years ago
  15. lilly21 Group Title
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    but you c in my book it has an answer or answers of min (0,-3) and max (2,1)

    • 2 years ago
  16. hartnn Group Title
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    i know, there is no global extrema, and so, here we find local extrema by substituting the endpoints. so put x=0 and x=2 and find f(x)

    • 2 years ago
  17. hartnn Group Title
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    *local = absolute

    • 2 years ago
  18. hartnn Group Title
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    whenever we don't get global extrema, we put endpoints....remember this.

    • 2 years ago
  19. lilly21 Group Title
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    i am utterly confused :[

    • 2 years ago
  20. hartnn Group Title
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    lets start over ?

    • 2 years ago
  21. lilly21 Group Title
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    yes please :]

    • 2 years ago
  22. hartnn Group Title
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    ok, absolute extrema means max or min points in the given interval.

    • 2 years ago
  23. hartnn Group Title
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    now to find min or max values, you take derivative of function and set it =0

    • 2 years ago
  24. hartnn Group Title
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    then you get values of x for which the function is min/max. if f'(x) cannot be equal to 0, then there is no global extrema ok ?

    • 2 years ago
  25. lilly21 Group Title
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    ok

    • 2 years ago
  26. lilly21 Group Title
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    or if its like 1/0 right?

    • 2 years ago
  27. hartnn Group Title
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    in that case, we can find 'local' or 'absolute' values at the endpoints, they become min/max values.

    • 2 years ago
  28. hartnn Group Title
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    yes.

    • 2 years ago
  29. lilly21 Group Title
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    so 2=0

    • 2 years ago
  30. hartnn Group Title
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    i can't think of an example when u get 1/0 after taking the derivative.

    • 2 years ago
  31. hartnn Group Title
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    here , you get f'(x) =2 we cannot equate this to 0

    • 2 years ago
  32. hartnn Group Title
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    because 2 can never =0 hence there is no extrema, or as we say, no global extrema

    • 2 years ago
  33. hartnn Group Title
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    but we can find absolute extrema, that is min/max in GIVEN INTERVAL

    • 2 years ago
  34. lilly21 Group Title
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    how do we find these?

    • 2 years ago
  35. hartnn Group Title
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    one of the end-point is x=2 there what is f(x) = ?

    • 2 years ago
  36. lilly21 Group Title
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    1?

    • 2 years ago
  37. hartnn Group Title
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    so the point is (2,1) and this is one of the extrema we don't know yet whether this is max or min

    • 2 years ago
  38. hartnn Group Title
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    now put other end point, x=0 what is f(x)

    • 2 years ago
  39. lilly21 Group Title
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    wait where did we get x=0?

    • 2 years ago
  40. hartnn Group Title
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    [0,2]

    • 2 years ago
  41. jaersyn Group Title
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    your interval [0,2]

    • 2 years ago
  42. hartnn Group Title
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    thats where i got x=2 also earlier

    • 2 years ago
  43. lilly21 Group Title
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    ooooooooo okay there will be 3 extrema right???

    • 2 years ago
  44. hartnn Group Title
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    how come 3 ? one for x=2, and one for x=0

    • 2 years ago
  45. lilly21 Group Title
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    o yeah my bad -_- :]

    • 2 years ago
  46. lilly21 Group Title
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    we do the same for 0 right ???? plug it into the orig equation? right?

    • 2 years ago
  47. jaersyn Group Title
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    you could just say there's no global min/max since the function is linear right?..

    • 2 years ago
  48. hartnn Group Title
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    yes.

    • 2 years ago
  49. hartnn Group Title
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    to both

    • 2 years ago
  50. jaersyn Group Title
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    k, thanks. double checking.

    • 2 years ago
  51. hartnn Group Title
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    now put other end point, x=0 what is f(x)

    • 2 years ago
  52. lilly21 Group Title
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    -3?

    • 2 years ago
  53. hartnn Group Title
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    so the other point is ?

    • 2 years ago
  54. hartnn Group Title
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    and which one should be min and which one should be max ?

    • 2 years ago
  55. lilly21 Group Title
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    0,-3 is min the other is max?

    • 2 years ago
  56. hartnn Group Title
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    yes, thats correct. clear with every step ?

    • 2 years ago
  57. lilly21 Group Title
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    yes sir or mam! :]

    • 2 years ago
  58. lilly21 Group Title
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    thanks so much!

    • 2 years ago
  59. hartnn Group Title
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    your welcome ^_^

    • 2 years ago
  60. lilly21 Group Title
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    :]

    • 2 years ago
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