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Math Help - [SOLVED] Find equations of the tangent line...

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    Junior Member moonman's Avatar
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    [SOLVED] Find equations of the tangent line...

    Find equations of the tangent line and normal line to the given curve at the specified point.

    Y = 2xe^(x) , (0,0)
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    Air
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    Quote Originally Posted by moonman View Post
    Find equations of the tangent line and normal line to the given curve at the specified point.

    Y = 2xe^(x) , (0,0)
    A tangent line is a straight line that touches a function at only one point. The slope of the tangent line (the gradient) at a point on the function is equal to the derivative of the function at the same point.

    y=2xe^x

    \frac{\mathrm{d}y}{\mathrm{d}x} = 2xe^x + 2e^x. At (0,0), The tangent gradient equals m = 2(0)e^0 + 2e^0 = 2

    Equation of tangent: y-0 = 2(x-0) \rightarrow y = 2x

    The equation of Normal line has the same coordinate of intersection (0,0) and the same y-intercept but the gradient is different. The gradient of the normal line is n = -\frac{1}{m} = -\frac{1}{2} where m is the gradient of the tangent line and n is the gradient of the normal line.

    This Equation of normal line: y-0 = -\frac12 (x-0) \rightarrow y = -\frac12 x
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