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Find the linearization of $\sqrt{x}$ at $x = 4$ \hfil \break
I.e, %%\hfil \break
find the best linear approximation of $\sqrt{x}$ for $x$ close to 
$4$.\hfil \break
I.e, find the equation of tangent line to $\sqrt{x}$ at $x = 4$.


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Approximate $\sqrt{5}$

Method 1:  Use equation of tangent line

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Method 2 (optional, but quicker):  Use $\Delta y \sim dy$

Recall: slope of secant line = ${\Delta y \over \Delta x}$

 $\Delta x = x + h - x$, \hfill~~ $\Delta y = f(x + h) - f(x) =
f(x + \Delta x) - f(x)$  

slope of tangent line = $f'(x) = {dy \over dx}$.  Thus $dy = f'(x)dx$.  

Let $\Delta x = dx$. Then  $\Delta y \sim dy$


$f(x + \Delta x) = f(x) + \Delta y \sim f(x) + dy$



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