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Math Help - exponential function

  1. #1
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    exponential function

    At what point on the given curve is the tangent line parallel to the line 3x - y = 2? y = 3 + 2ex5x


    How do i do this?
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  2. #2
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    Quote Originally Posted by rhcp1231 View Post
    At what point on the given curve is the tangent line parallel to the line 3x - y = 2? y = 3 + 2ex5x


    How do i do this?
    You need to set the derivative of the curve to the slope of the given line and solve for x. By the way is 2e^x or 2ex?
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  3. #3
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    2e^x

    so the derivative is 2e^x-5, how do i solve for x for that?
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  4. #4
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    Quote Originally Posted by rhcp1231 View Post
    2e^x

    so the derivative is 2e^x-5, how do i solve for x for that?
    3=2e^x-5

    8=2e^x

    e^x=4

    x=ln(4)

    Then just plug that into the original equation for the curve and you have the point where te tangent line is parallel to the given line.
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  5. #5
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    Quote Originally Posted by Keithfert488 View Post
    3=2e^x-5

    8=2e^x

    e^x=4

    x=ln(4)



    and the 3 comes from 3x - y = 2 right?
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  6. #6
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    Quote Originally Posted by rhcp1231 View Post
    and the 3 comes from 3x - y = 2 right?
    Yes. If you put the equation into slope intercept format (y=mx+b) you find that y=3x-2 so the slope is three.
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  7. #7
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    Quote Originally Posted by Keithfert488 View Post
    Yes. If you put the equation into slope intercept format (y=mx+b) you find that y=3x-2 so the slope is three.
    sweet thanks for the help
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