Linearization
posted by Michael .
Find the linear approximation of the function f(x) = √16x at a = 0

What is a? It does not appear in your formula for f(x)
Do you mean
f(x) = (sqrt16)  x or sqrt(16x)?
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)/(16x)^1/2 = 1/8
In linear approximation,
f(x) = f(0) + f'(0)*x
= 4  (x/8)
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