Use linear approximation, i.e. the tangent line, to approximate $\sqrt[3] { 8.1 }$ as follows. Let $f(x) = \sqrt[3] x$ and find the equation of the tangent line to $f(x)$ at $x = 8$ in the form $y = mx+b$.

Note: The values of $m$ and $b$ are rational numbers which can be computed by hand. You need to enter expressions which give $m$ and $b$ exactly. You may not have a decimal point in the answers to either of these parts.

$m$ =

$b$ =

Using these values, find the approximation.

$\sqrt[3] {8.1} \approx$

Note: You can enter decimals for the last part, but it will has to be entered to very high precision (correct for 6 places past the decimal point).