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Find the linear approximation of the function f(x) = √16-x at a = 0

  • Linearization - ,

    What is a? It does not appear in your formula for f(x)

    Do you mean
    f(x) = (sqrt16) - x or sqrt(16-x)?

    The first case is trivial: 4 -x.

    For the second case, use the Taylor series formula.

    At x=0, the derivative of f(x) is
    f'(x) =
    (-1/2)/(16-x)^1/2 = -1/8

    In linear approximation,
    f(x) = f(0) + f'(0)*x
    = 4 - (x/8)

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