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Math Help - Tangent line

  1. #1
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    Tangent line

    I have a calc test tomorrow and I'm stuck on this practice problem. Please help. He gave us the answer which is y=2x+1, but I don't know how to do it. Please help. I have an idea of how he got it, but the e threw me off.


    Find the indicated tangent line.

    Find the tangent line to the graph of f(x) = e^2x at the point (0, 1).



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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by aphan19 View Post
    I have a calc test tomorrow and I'm stuck on this practice problem. Please help. He gave us the answer which is y=2x+1, but I don't know how to do it. Please help. I have an idea of how he got it, but the e threw me off.


    Find the indicated tangent line.

    Find the tangent line to the graph of f(x) = e^2x at the point (0, 1).


    Use the formula for a tangent line

    y-f(x_0)=f'(x_0)(x-x_0)

    Using x_0=0

    f(x_0)=1

    and f'(x_0)=f'(0)
    were f'(x)=2e^{2x}
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by aphan19 View Post
    I have a calc test tomorrow and I'm stuck on this practice problem. Please help. He gave us the answer which is y=2x+1, but I don't know how to do it. Please help. I have an idea of how he got it, but the e threw me off.


    Find the indicated tangent line.

    Find the tangent line to the graph of f(x) = e^2x at the point (0, 1).


    To find the tangent line, we first need to know the slope. We can find out the slope by finding f'(x) at x=0.

    \frac{dy}{dx}=2e^{2x}. At x=0, we get \frac{dy}{dx}=2.

    Now that we have the slope, now find the equation of the tangent line:

    y-(1)=(2)(x-(0))\rightarrow y=2x+1.

    Hoped that answered your question!!
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