Chapter 4.3, Problem 3QCE

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

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

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

(c) The graph is increasing on the interval $\text{\_\_\_\_\_\_\_\_}$ .

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

(e) The relative minimum point on the graph is $\text{\_\_\_\_\_\_\_\_}$ .

(f) The relative maximum point on the graph is $\text{\_\_\_\_\_\_\_\_}$ .

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