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Math Help - Natural Logarithm: find the point on the curve

  1. #1
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    Natural Logarithm: find the point on the curve

    Question: Find the point on the curve y=e^2x+1 where the tangent is parallel to the line y=2ex.

    Please help. Thanks.
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  2. #2
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    Re: Natural Logarithm: find the point on the curve

    Quote Originally Posted by onehundredpercenteffort View Post
    Question: Find the point on the curve y=e^2x+1 where the tangent is parallel to the line y=2ex.
    The graph of y = e^2x+1 is a straight line, so a tangent to it is itself. Since the slope of y = e^2x+1, which is e^2, is different from the slope of y = 2ex, which is 2e, no tangent to y = e^2x+1 is parallel to y = 2ex.
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    Re: Natural Logarithm: find the point on the curve

    Quote Originally Posted by onehundredpercenteffort View Post
    Question: Find the point on the curve y=e^2x+1 where the tangent is parallel to the line y=2ex.
    Is the function e^{2x}+1\text{ or }e^{2x+1} or something else altogether?
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  4. #4
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    Re: Natural Logarithm: find the point on the curve

    Whatever the function, you need to take the derivative and set it equal to 2e.

    - Hollywood
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    Re: Natural Logarithm: find the point on the curve

    i understand that i have to find the derivative which was y'=2e^2x+1 and since the tangent is parallel, the slopes will be the same. But how can i find the point??
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    Re: Natural Logarithm: find the point on the curve

    Quote Originally Posted by onehundredpercenteffort View Post
    i understand that i have to find the derivative which was y'=2e^2x+1 and since the tangent is parallel, the slopes will be the same. But how can i find the point??
    Why do you refuse to tell us what the function really is?

    What is the correct way to read the function? See reply #3.
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  7. #7
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    Re: Natural Logarithm: find the point on the curve

    You set y' = 2e^(2x+1) = 2e and solve for x. The slope of the other curve, y=2ex, is 2e. So x=0, right?

    All three of us were confused about what the function was; you really should have cleared that up in addition to asking for clarification.

    - Hollywood
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