## Calculus (3rd Edition)

$$y=108x-216.$$
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 $$y=108x-216.$$