Use linear approximation to approximate $\sqrt {36.1}$ as follows.

Let $f(x) = \sqrt x$. The equation of the tangent line to $f(x)$ at $x = 36$ can be written in the form $y = mx+b$. Compute $m$ and $b$.

$m=$
$b=$

Using this find the approximation for $\sqrt {36.1}$.

Answer: