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anonymous

  • one year ago

Find the extreme values of the function and where they occur

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  1. anonymous
    • one year ago
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    \[1/(x^2-1)\]

  2. anonymous
    • one year ago
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    @Loser66

  3. Loser66
    • one year ago
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    What is the definition of extreme value?

  4. anonymous
    • one year ago
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    The relative (or local) max/min points.

  5. Loser66
    • one year ago
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    yes, so that just take derivative of f

  6. anonymous
    • one year ago
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    Only 1 derivative?

  7. Loser66
    • one year ago
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    let it =0, find x replace that x into the original function, and you are done.

  8. Loser66
    • one year ago
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    first derivative only.

  9. anonymous
    • one year ago
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    Oh! So when i write the answer i just say y=??

  10. Loser66
    • one year ago
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    When you get the result (x =0) , your conclusion is f(x) has extreme value and x =0 and f(0) = -1

  11. Loser66
    • one year ago
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    *at, not and f(x) has extreme value AT x =0 ,....

  12. anonymous
    • one year ago
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    ohh, okay, let me solve it.

  13. anonymous
    • one year ago
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    \[f'(x)=\left(\begin{matrix}-2x \\ (x^2-1)^2\end{matrix}\right)\]

  14. anonymous
    • one year ago
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    correct?

  15. Loser66
    • one year ago
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    It is NOT a matrix, it is a fraction. but it is correct.

  16. anonymous
    • one year ago
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    yeah sorry, meant to be a fraction

  17. anonymous
    • one year ago
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    so how do i solve for x from here?

  18. Loser66
    • one year ago
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    you solve for f' =0 iff the numerator =0

  19. Loser66
    • one year ago
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    and the numerator is -2x =0 iff x =0, right?

  20. anonymous
    • one year ago
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    correct

  21. anonymous
    • one year ago
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    so x=0?

  22. Loser66
    • one year ago
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    plug back to original one to find value of f(0)=??

  23. anonymous
    • one year ago
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    -1?

  24. Loser66
    • one year ago
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    yup

  25. anonymous
    • one year ago
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    So the answer doesn't have to be like, absolute max = ?? absolute min= ??

  26. anonymous
    • one year ago
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    sorry just making sure haha

  27. amoodarya
    • one year ago
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    |dw:1437521757173:dw|

  28. Loser66
    • one year ago
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    If you have 2 solutions, plug back and compare which one is larger, the larger one is max, the lesser one is min In this case, you have only 1 solution. You have no comparison, how to say whether it is max or min?

  29. amoodarya
    • one year ago
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    |dw:1437521827659:dw| this is sketch of f(X) so x=0 is not abs max

  30. anonymous
    • one year ago
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    So no absolute max or min?

  31. Loser66
    • one year ago
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    yup, just local

  32. anonymous
    • one year ago
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    so is 0 the local max or local min? I'm confused sorry

  33. amoodarya
    • one year ago
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    |dw:1437523053515:dw|local max

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