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    Stuck again.

    Question:
    The maximum point on the curve with the equation y=xsin^0.5x where 0<x<pi is A. Show that the x coordinate of A satisfies the equation 2tanx+x=0.


    I've differentiated it to sin^0.5x +xcosx/2sin^0.5x, but cant work out how to get the maximum point.
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    set the differential equal to zero, take out sinx as a common factor
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    (Original post by LukeMontgomery)
    Stuck again.

    Question:
    The maximum point on the curve with the equation y=xsin^0.5x where 0<x<pi is A. Show that the x coordinate of A satisfies the equation 2tanx+x=0.


    I've differentiated it to sin^0.5x +xcosx/2sin^0.5x, but cant work out how to get the maximum point.
    set **sin^0.5x +xcosx/2sin^0.5x to zero

    multiply each term by *sin^0.5x

    to get tanx you need to think of sinx/cosx ....*
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    (Original post by the bear)
    set **sin^0.5x +xcosx/2sin^0.5x to zero

    multiply each term by *sin^0.5x

    to get tanx you need to think of sinx/cosx ....*
    If I times both sides by sin^0.5x then I get sinx+xcosx/2=0

    What do I do from there?
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    (Original post by LukeMontgomery)
    If I times both sides by sin^0.5x then I get sinx+xcosx/2=0

    What do I do from there?
    you need to somehow get tanx to appear.... *
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    (Original post by the bear)
    you need to somehow get tanx to appear.... *
    sinx+xcosx/2=0

    2sinx+xcosx=0

    2sinx/cosx+xcosx/cosx=0

    =2tanx+x=0

    Ok so I've done that, but how do I work out the x coordinate of A.
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    (Original post by LukeMontgomery)
    sinx+xcosx/2=0

    2sinx+xcosx=0

    2sinx/cosx+xcosx/cosx=0

    =2tanx+x=0

    Ok so I've done that, but how do I work out the x coordinate of A.
    You don't have to. It simply asks you to show that it satisfies that equation and you've done it. It's a transcendental equation anyhow so you cannot solve it using analytical methods, unless you say x=0 but that's not the only solution.
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    (Original post by RDKGames)
    You don't have to. It simply asks you to show that it satisfies that equation and you've done it. It's a transcendental equation anyhow so you cannot solve it using analytical methods, unless you say x=0 but that's not the only solution.
    Ok good, thanks!
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    you could use something like the Newton-Raphson method to solve it after that.
 
 
 
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