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Math Help - Curve sketching

  1. #1
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    Curve sketching

    Show that the curve with equation y = 3\ cosh\ x - x\ sinh\ x has a minimum point A on the y-axis. Find the coordinates of A. Show further that the curve has another stationary value between x = 1.9 and x = 3. Sketch the curve.

    Iíve done all except curve sketching. How can I sketch this curve? Actually what the process?
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  2. #2
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    Quote Originally Posted by geton View Post
    Show that the curve with equation y = 3\ cosh\ x - x\ sinh\ x has a minimum point A on the y-axis. Find the coordinates of A. Show further that the curve has another stationary value between x = 1.9 and x = 3. Sketch the curve.

    Iíve done all except curve sketching. How can I sketch this curve? Actually what the process?
    First try substituting the definitions of cosh x and sinh x in terms of exponentials. Simplify. Consider key features and asymptotic behaviour.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    First try substituting the definitions of cosh x and sinh x in terms of exponentials. Simplify. Consider key features and asymptotic behaviour.
    May be I need more information, because Iím so weak on this regard.

    By the way, I simplified,

    y = 3/2 (e^x + e^-x) Ė x/2 (e^x - e^-x)
    = e^2x (3/2 Ė x/2) + 1/2 (3/2 + x/2)

    What to do next? As I get a minimum point A is (0, 3). And another stationary point lies between 1.9 and 2. Have to working on this to find 2nd stationary point?


    Do you have any suggestions/notes/useful websites to learn this kind of stuff, will help me lot to understand.
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