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Math Help - Hyperbolic maximum turning point

  1. #1
    Super Member craig's Avatar
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    Hyperbolic maximum turning point

    Hi, need a bit of help with this question.

    The curve y = -x + \tanh{48x}, x \ge 0 has a maximum turning point at A, find the x co-ordinates of A in exact logarithmic form.

    Differentiated the equation to get x = \frac{ln{(7 \pm 4\sqrt{3})}}{49}, which turns out to be right.

    In the answers though, they only have x = \frac{ln{(7 + 4\sqrt{3})}}{49}, at first I though this was because you cannot take a natural log of a minus number, but 7 - 4\sqrt{3} is a positive number.

    Any ideas?

    Thanks in advance.
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  2. #2
    Super Member craig's Avatar
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    I could differentiate it again and then see whether it is a positive or negative number, to determine whether it is a maximum or minimum, but was just wondering if there was an easier method than this.

    Also, they have not made any reference to this in the answers :S
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  3. #3
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    Grandad's Avatar
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    Turning points

    Hi Craig -

    I haven't done the differentiation, but presumably the other root gives a minimum?

    Grandad
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    Super Member craig's Avatar
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    Quote Originally Posted by Grandad View Post
    Hi Craig -

    I haven't done the differentiation, but presumably the other root gives a minimum?

    Grandad
    Hi Grandad thanks for the reply. That's what I thought, just wondering if there is an obvious way that you just know, something that I'd missed
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