Chapter 4.3, Problem 1QCE

Let $f\left(x\right)=\frac{3\left(x+1\right)\left(x-3\right)}{\left(x+2\right)\left(x-4\right)}$ . Given that $f^{\prime }\left(x\right)=\frac{-30\left(x-1\right)}{{\left(x+2\right)}^2{\left(x-4\right)}^2},f^{″}\left(x\right)=\frac{90\left(x^2-2x+4\right)}{{\left(x+2\right)}^3{\left(x-4\right)}^3}$ determine the following properties of the graph of $f$ .

(a) The $x\text{-}$ and y-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) The relative maximum point on the graph is $\text{\_\_\_\_\_\_\_\_}$ .