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Math Help - Tangent to the Curve

  1. #1
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    Tangent to the Curve

    Greetings,

    This should be a relatively easy question, but, unfortunately, I am struggling with solving it. I understand the forum is used purely for guiding someone. However, I have the GRE Math Subject test in 13hrs and need to see how this problem is worked out if someone wouldn't mind.

    The question is:

    For what value of b is the line \displaystyle y=10x tangent to the curve \displaystyle y=e^{bx} at some point in the xy-plane?

    Thanks again.
    Last edited by dwsmith; November 12th 2010 at 03:34 PM.
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  2. #2
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    Quote Originally Posted by dwsmith View Post
    Greetings,

    This should be a relatively easy question, but, unfortunately, I am struggling with solving it. I understand the forum is used to purely for guiding someone. However, I have the GRE Math Subject test in 13hrs and need to see how this problem is worked out if someone wouldn't mind.

    The question is:

    For what value of b is the line \displaystyle y=10x tangent to the curve \displaystyle y=e^{bx} at some point in the xy-plane?

    Thanks again.
    tangent line "touches" the exponential function ...

    e^{bx} = 10x

    slope of the curve = slope of the tangent line

    be^{bx} = 10


    \displaystyle \frac{be^{bx}}{e^{bx}} = \frac{10}{10x}

    \displaystyle b = \frac{1}{x}

    e^{bx} = 10x

    e = 10x

    \displaystyle x = \frac{e}{10}

    line is tangent to the curve at \displaystyle \left(\frac{e}{10} , e\right)

    \displaystyle b = \frac{10}{e}
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    Quote Originally Posted by skeeter View Post
    tangent line "touches" the exponential function ...

    \displaystyle \frac{be^{bx}}{e^{bx}} = \frac{10}{10x}
    Why did you divide the derivatives by the original equations?
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    Why did you divide the derivatives by the original equations?
    to get rid of e^{bx}
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