Analyse the model $by$ responding $to$ the following.

Show that $p^{\text{'}}(t)=3200\frac{t}{(4+t^2{)}^2}*(\frac{?}{2}$ points$)$

Show that $p^{}(t)=3200\frac{4-3t^2}{(4+t^2{)}^3}*(\frac{?}{2}$ points$)$

Solve for the vertical and horizontal asymptotes. $(\frac{?}{4}$ points$)$

Solve for the critical point$(s).(\frac{?}{3}$ points$)$

Solve for the intervals $of$ increase and decrease. $(\frac{?}{3}$ points$)$

Solve for the local maximums $an\frac{d}{o}r$ minimums. $(\frac{?}{2}$ points$)$

Solve for the intervals $of$ concavity. $(\frac{?}{4}$ points$)$

Solve for the inflection point$(s).(\frac{?}{2}$ points$)$