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lilly21

  • 3 years ago

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

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  1. infoshark
    • 3 years ago
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    Familiar with the derivative ? can you take the derivative of f(x), if so, what do you get ?

  2. lilly21
    • 3 years ago
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    2

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

  4. lilly21
    • 3 years ago
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    at y=0???

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

  6. lilly21
    • 3 years ago
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    nope

  7. infoshark
    • 3 years ago
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    any max extrema then ?

  8. infoshark
    • 3 years ago
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    abs*

  9. lilly21
    • 3 years ago
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    im kinda of confused by ur question :[

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

  11. lilly21
    • 3 years ago
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    1 ?

  12. hartnn
    • 3 years ago
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    thats correct :)

  13. lilly21
    • 3 years ago
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    thats it?

  14. hartnn
    • 3 years ago
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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.....

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

  16. hartnn
    • 3 years ago
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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)

  17. hartnn
    • 3 years ago
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    *local = absolute

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

  19. lilly21
    • 3 years ago
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    i am utterly confused :[

  20. hartnn
    • 3 years ago
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    lets start over ?

  21. lilly21
    • 3 years ago
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    yes please :]

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

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

  24. hartnn
    • 3 years ago
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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 ?

  25. lilly21
    • 3 years ago
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    ok

  26. lilly21
    • 3 years ago
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    or if its like 1/0 right?

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

  28. hartnn
    • 3 years ago
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    yes.

  29. lilly21
    • 3 years ago
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    so 2=0

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

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

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

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

  34. lilly21
    • 3 years ago
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    how do we find these?

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

  36. lilly21
    • 3 years ago
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    1?

  37. hartnn
    • 3 years ago
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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

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

  39. lilly21
    • 3 years ago
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    wait where did we get x=0?

  40. hartnn
    • 3 years ago
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    [0,2]

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

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

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

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

  45. lilly21
    • 3 years ago
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    o yeah my bad -_- :]

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

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

  48. hartnn
    • 3 years ago
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    yes.

  49. hartnn
    • 3 years ago
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    to both

  50. jaersyn
    • 3 years ago
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    k, thanks. double checking.

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

  52. lilly21
    • 3 years ago
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    -3?

  53. hartnn
    • 3 years ago
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    so the other point is ?

  54. hartnn
    • 3 years ago
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    and which one should be min and which one should be max ?

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

  56. hartnn
    • 3 years ago
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    yes, thats correct. clear with every step ?

  57. lilly21
    • 3 years ago
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    yes sir or mam! :]

  58. lilly21
    • 3 years ago
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    thanks so much!

  59. hartnn
    • 3 years ago
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    your welcome ^_^

  60. lilly21
    • 3 years ago
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    :]

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