Chapter 4.3, Problem 2QCE

Let $f\left(x\right)=\frac{x^2-4}{x^{8/3}}$ . Given that $f^{\prime }\left(x\right)=\frac{-2\left(x^2-16\right)}{3x^{11/3}},f^{″}\left(x\right)=\frac{2\left(5x^2-176\right)}{9x^{14/3}}$ determine the following properties of the graph of $f$ .

(a) The x-intercepts are $\text{\_\_\_\_\_\_\_\_}$ .

(b) The vertical asymptotes are $\text{\_\_\_\_\_\_\_\_}$ .

(c) The horizontal asymptote is $\text{\_\_\_\_\_\_\_\_}$ .

(d) The graph is above the x-axis on the intervals $\text{\_\_\_\_\_\_\_\_}$ .

(e) The graph is increasing on the intervals $\text{\_\_\_\_\_\_\_\_}$ .

(f) The graph is concave up on the intervals $\text{\_\_\_\_\_\_\_\_}$ .

(g) Inflection points occur at $x=\text{\_\_\_\_\_\_\_\_}$ .