1. ## Linear Approximation

Find the linear approximation, for...
$y=mx+b, to f(x) = \sqrt[3]{3x-1}$
at the point x=3

Ok, so
$f(3)=2$
$f'(x)=3x-1$
$f'(3)=8$
now to solve for y=mx+b?..
$2=8(3)+b$
$b=-22$
$y=8x-22$

this is apparently wrong. What am I doing wrong here?

2. I think you got the wrong expression for f'(x)

$f(x) = (3x - 1)^{\frac13}$

$f'(x) = \dfrac13 (3x-1)^{-\frac23} \cdot 3 = (3x-1)^{-\frac23} = \sqrt[3]{\dfrac{1}{(3x-1)^2}}$