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Math Help - finding the equation of a tangent line

  1. #1
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    Exclamation finding the equation of a tangent line

    help please and thank you!!


    y=e^x

    find the equation of the tangent line at x=0
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  2. #2
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    Quote Originally Posted by cottekr View Post
    help please and thank you!!


    y=e^x

    find the equation of the tangent line at x=0
    A tangent line is a straight line, so is of the form

    y=mx+c where m is the gradient and c is the y-intercept.

    To find the gradient of this tangent, we need to differentiate the function and evaluate it at that point.

    y=e^x so \frac{dy}{dx} = e^x.

    At the point x=0, \frac{dy}{dx} = e^0 = 1.

    So the gradient of the tangent at x=0 is 1.

    We know that when x=0, y=1, so the y-intercept is 1.

    Thus the equation of the tangent is

    y = x + 1
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  3. #3
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    Eqn of tangent line: y-y_1 = m(x-x_1) where m is the gradient at the point (x_1 , y_1)

    When x_1=0, y= e^0 = 1

    \frac{dy}{dx} = e^x at x=0, \frac{dy}{dx} = 1

    So the equation of the tangent line is

    y-1 = 1(x-0)

    y=x+1
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