#### Answer

$$ y=108x-216.$$

#### Work Step by Step

Since $ f(x)=x^4$, then $ y=f'(x)=4x^3$. To find the tangent line of $ y $, we have
$ y'=12x^2 \Longrightarrow m=y'(3)=108.$
The tangent at $ x=3$ is given by
$$ y=108x+c.$$
To find $ c $, we have $ y(3)= 4(27)=108$ and hence $108=108(3)+c $, then $ c=-216$.
Then the line is $$ y=108x-216.$$