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Math Help - tangent line

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    tangent line

    Assume that f(x) is differentiable at x=a.state the equation of tangent line to the graph of f(x) at point (a,f(a))
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    Quote Originally Posted by bobby77 View Post
    Assume that f(x) is differentiable at x=a.state the equation of tangent line to the graph of f(x) at point (a,f(a))
    The equation of a line is
    y = mx + b

    We know the slope of the function at (a, f(a)): it is simply f'(a). Thus

    f(a) = f'(a)*a + b

    b = f(a) - f'(a)*a

    So
    y = f'(a)x + [f(a) - f'(a)*a]

    -Dan
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    You can also use the formula,
    If m is slope and (x_0,y_0) is point then equation is,
    y-y_0=m(x-x_0)

    Thus,
    m=f'(a)
    x_0=a
    y_0=f(a)

    Thus,
    y=f'(a)x-f'(a)a+f(a)
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