Chapter 10.5, Problem 24E

To determine

To calculate: The horizontal and vertical asymptote, relative minimum, relative maximum and points of inflection for the provided function $f\left(x\right)=\frac{3x^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{x+1}$ and the first derivative $f\text{'}\left(x\right)=\frac{2-x}{x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left(x+1\right)}^2}$ and second derivative $f\text{'}\text{'}\left(x\right)=\frac{2\left(2x^2-8x-1\right)}{3x^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left(x+1\right)}^3}$ and sketch its graph.