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Math Help - At what point on the given curve is the tangent line parallel to the line 3x - y = 3?

  1. #1
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    At what point on the given curve is the tangent line parallel to the line 3x - y = 3?

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

    y = 2 + 2ex3x

    get x and y.


    what I did so far:

    rearranged 3x=y=3 to get y=3x-3, which shows the slope is 3, so i need to find where my tangent line has a slope of 3 on the line 2+2e^x-3 i think.
    How would i proceed? Thanks.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Evan.Kimia View Post
    At what point on the given curve is the tangent line parallel to the line 3x - y = 3?

    y = 2 + 2ex3x

    get x and y.


    what I did so far:

    rearranged 3x=y=3 to get y=3x-3, which shows the slope is 3, so i need to find where my tangent line has a slope of 3 on the line 2+2e^x-3 i think.
    How would i proceed? Thanks.
    It is commonly known that if everything is permissable (defined, differentiable, etc.) the slope of the tangent line at x=x_0 for a function f(x) is just f'(x_0)

    So you want to find the point x_0 such that \frac{d}{dx}\left[2+2e^x-3x\right]=3. Can you do that?
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    ok, so would i do this....

    find deriv. of 2+2e^x-3x

    = 0 + 2e^x (product rule) -3 = 3

    then add 3 both sides, get 2e^x = 6

    divide by 2, get e^x=3

    ln(3)=1.0986?
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Evan.Kimia View Post
    ok, so would i do this....

    find deriv. of 2+2e^x-3x

    = 0 + 2e^x (product rule) -3 = 3

    then add 3 both sides, get 2e^x = 6

    divide by 2, get e^x=3

    ln(3)=1.0986?
    Exactly! One minor note....how did you get \frac{d}{dx}\left[e^x\right]=e^x via product rule?
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  5. #5
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    I got it. For those who were as confused as i was, just plug in the x value into the equation of the curve to get your y value.
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  6. #6
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    my bad, lazy typing. I mean product rule at first for 2e^x, then i know the derivative of e^x is itself, which is then multiplied by 2 according to the constant multiple rule.
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