Posted by Michael on Thursday, November 11, 2010 at 9:56pm.
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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