Q$1)(30$ pts $.)$ Let $f$:$\frac{R}{\frac{?}{?}}\{-3\mathrm{.}5\}longrightarrowR$ be a function satisfying the following conditions:

$f(0)=1,f(7)=0,f(-3)$ and $f(5)$ are undefined

$\underset{x{5}^{-}}{lim}f(x)=,\underset{x{5}^{-}}{lim}f(x)=\underset{x}{lim}f(x)=-,\underset{x-}{lim}f(x)=4\underset{x-3}{lim}f(x)=2$

$f^{\text{'}\text{'}}(x)<mn>0</mn>$ for

$f^{\text{'}\text{'}}(7)=0$

$(b)$ Find the inflection point$(s)$ and the intervals where $fis$ concave upward and the intervals where $fis$ concave downward.

$\begin{array}{cc}?& \\ f^{\text{'}\text{'}}& \\ f& \end{array}$

fis concave downard $of$

$fis$ concave upward $on.$

$1isan$ inflection point $off.$

$(c)$ Find all vertical and horizontal asymptoter $off,if$ there exist any:

$(d)$ Sloetch the graph $ofy=f(x).Be$ sure that all local maximu$\frac{m}{m}$inimum, inflection points, asymptotes and interespts are clearly labelled $on$ the graph.

$\begin{array}{cc}?& ?\\ f^{\text{'}}& ?\\ f^{\text{'}\text{'}}& ?\\ f& ?\\ f& ?\end{array}-3,$ and $5$

$f^{\text{'}\text{'}}(7)=0$

$(b)$ Find the inflection point$(s)$ and the intervals where $fis$ concave upward and the intervals where $fis$ concave downward.

$\begin{array}{cc}?& \\ f^{\text{'}\text{'}}& \\ f& \end{array}$

fis concave downard $of$

$fis$ concave upward $on.$

$1isan$ inflection point $off.$

$(c)$ Find all vertical and horizontal asymptoter $off,if$ there exist any:

$(d)$ Sloetch the graph $ofy=f(x).Be$ sure that all local maximu$\frac{m}{m}$inimum, inflection points, asymptotes and interespts are clearly labelled $on$ the graph.

$\begin{array}{cc}?& ?\\ f^{\text{'}}& ?\\ f^{\text{'}\text{'}}& ?\\ f& ?\\ f& ?\end{array}0$

$f^{\text{'}}(0)=0$

$f^{\text{'}\text{'}}(x)<mn>0</mn>$ for and $x>7$

$f^{\text{'}\text{'}}(x)>0$ for $-3,$ and $5$

$f^{\text{'}\text{'}}(7)=0$

$(b)$ Find the inflection point$(s)$ and the intervals where $fis$ concave upward and the intervals where $fis$ concave downward.

$\begin{array}{cc}?& \\ f^{\text{'}\text{'}}& \\ f& \end{array}$

fis concave downard $of$

$fis$ concave upward $on.$

$1isan$ inflection point $off.$

$(c)$ Find all vertical and horizontal asymptoter $off,if$ there exist any:

$(d)$ Sloetch the graph $ofy=f(x).Be$ sure that all local maximu$\frac{m}{m}$inimum, inflection points, asymptotes and interespts are clearly labelled $on$ the graph.

and $x>5$

$f^{\text{'}}(x)>0$ for $0$

$f^{\text{'}}(0)=0$

$f^{\text{'}\text{'}}(x)<mn>0</mn>$ for and $x>7$

$f^{\text{'}\text{'}}(x)>0$ for $-3,$ and $5$

$f^{\text{'}\text{'}}(7)=0$

$(b)$ Find the inflection point$(s)$ and the intervals where $fis$ concave upward and the intervals where $fis$ concave downward.

$\begin{array}{cc}?& \\ f^{\text{'}\text{'}}& \\ f& \end{array}$

fis concave downard $of$

$fis$ concave upward $on.$

$1isan$ inflection point $off.$

$(c)$ Find all vertical and horizontal asymptoter $off,if$ there exist any:

$(d)$ Sloetch the graph $ofy=f(x).Be$ sure that all local maximu$\frac{m}{m}$inimum, inflection points, asymptotes and interespts are clearly labelled $on$ the graph.

$\begin{array}{cc}?& ?\\ f^{\text{'}}& ?\\ f^{\text{'}\text{'}}& ?\\ f& ?\\ f& ?\end{array}$