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    pop000's Avatar
    pop000 Posts: 352, Reputation: 6
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    #1

    Dec 9, 2010, 06:34 AM
    Two Questions about function
    1) how I find the cutting point with X axis of the function:6*sqrtIXI-X-8
    I think is x=0 but I don't know how to show the way of it.

    2)how I prove that the function:f(x)=cotx-tanx, are Continuous in(0;pi/2).
    and there is no any Absolute minimum or Maximum.

    thanks.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Dec 9, 2010, 07:15 AM

    1. No, the function should be equal to zero, not x. And you didn't make use of proper brackets...

    Is that it?



    2.











    You should know that cot(2x) is continuous between 0 and pi/2.
    pop000's Avatar
    pop000 Posts: 352, Reputation: 6
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    #3

    Dec 9, 2010, 07:56 AM
    'well yes I know in General that cotx are continuous between (0 and pi/2] and tanx are continuous between (-pi/2;pi/2).

    But how I prove that there is no Absolute minimum or Maximum.
    But there are local minimum or Maximum point

    And really thanks about all you'r answers in every Subject almost :)
    pop000's Avatar
    pop000 Posts: 352, Reputation: 6
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    #4

    Dec 9, 2010, 07:59 AM
    by the way I mean x=4 is the point that the function are cutting the X axis
    but how I show the way?

    thanks
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #5

    Dec 9, 2010, 08:54 AM

    Hm... I have seen this notation, but I'm afraid I won't be able to help you further for part 2 =/, sorry for that... and cot(x) is continuous for (0 and pi] while cot(2x) is continuous for (0 and pi/2], if I got that notation right.

    1.

    There are three solutions, one of which is indeed x = 4









    This gives:

    or

    or

    or

    or

    or

    You get x = 4, x = 16, and

    Using these in the original equation, only x = 4, 16 and are correct.
    pop000's Avatar
    pop000 Posts: 352, Reputation: 6
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    #6

    Dec 9, 2010, 09:15 AM
    Comment on Unknown008's post
    Thanks now I Understand.

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