Chapter 3 - Applications of Differentiation - 3.3 How Derivatives Affect the Shape of a Graph - 3.3 Exercises - Page 229: 45

$(3,\infty)$

$f$ is increasing on the interval(s) on which $f'(x)>0$. The nonnegative factors $(x+1)^{2}$ and $(x-6)^{4}$ do not affect the sign of $f'(x)$ = $(x+1)^{2}(x-3)^{5}(x-6)^{4}$. So $f'(x)$ $\gt$ $0$ => $(x-3)^{5}$ $\gt$ $0$ => $x-3$ $\gt$ $0$ => $x$ $\gt$ $3$ Thus $f$ is increasing on the interval $(3,\infty)$.