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Representing a function as a Taylor series of it’s derivative.
In my lecture notes, there is a Taylor series of a function $f$ of the form
$$f(x) = f(c) + f'(c) (x – c)$$
for some $c \in \mathbb R$. I can’t quite figure out how to expand this in my head.
To clarify, I could expand the right hand side, say
$$\begin{align*}
&= f'(c) (x – c)\\
&= f'(c)(x – c) – f”(c)(x – c)^2/2\\
&= f'(c)x – f'(c)c + f'(c)c – f”(c)(x – c)^2/2
\end{align*}$$
and this would equate to
$$f(x) = f(c) + f'(c)x – f'(c)c + f'(c)c – f”(c)(x – c)^2/2$$
But it isn’t the right expansion.
A:
Your first expansion is correct. Note that
\begin{align}
f'(c) x – f'(c) c &= x f'(c) – f'(c) c \\
&= x f'(c) – f'(c)^2 x/2
\end{align}
Clindamycin incorporation into the skin and subcutaneous tissue of healthy volunteers.
Clindamycin’s previously demonstrated efficacy in a variety of superficial and deep infections led to a number of in vivo studies to better elucidate the drug’s penetration across skin and its pharmacokinetic behavior in the subcutis. The objective of this study was to determine the feasibility of using clindamycin powder for topical applications, the ability of clindamycin to penetrate into the subcutis, and its terminal half-life. Two applications of clindamycin hydrochloride powder were used on 36 volunteers. Each volunteer was given a pair of powder-applied, 1.5 g clindamycin-treated areas.
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