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Math Help - How do I show that 1/n^(1/4) is decreasing?

  1. #1
    s3a
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    How do I show that 1/n^(1/4) is decreasing?

    I tried to use the first derivative test. d/dx n^(-1/4) = -1/4 * n^(-5/4)

    -1/4 * n^(-5/4) = 0
    n => does not exist

    If it equalled to 0 for exampel then I could show that for n>0, the output is negative but in this case, what can I do?

    Any input would be greatly appreciated!
    Thanks in advance!
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  2. #2
    Senior Member Dinkydoe's Avatar
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    I don't quite see your problem:

    the function f(x)= x^{-1/4} is decreasing since f'(x)=-\frac{1}{4}x^{-5/4} < 0 for x> 0.

    Thus the sequence x_n =n^{-1/4} must decrease.
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  3. #3
    s3a
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    I was trying to equate it to 0 and then plug in something larger but now I realize you can just inequalities. Thanks.
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