Suppose that $f$ is a continuous function that is twice$-$differentiable for $x0$ and $x6$ and that satisfies the following conditions:

$(1)f(0)=0,f(4)=2\sqrt[3]{4},f(6)=0$

$(2)f^{\text{'}}(4)=0,\underset{x{0}^{-}}{lim}{f}^{\text{'}}(x)=-,\underset{x{0}^{+}}{lim}{f}^{\text{'}}(x)=,\underset{x6}{lim}{f}^{\text{'}}(x)=-$

$(3)f^{\text{'}}(x)<mn>0</mn>$ for $x<mn>0</mn>$;$f^{\text{'}}(x)>0$ for ;$f^{\text{'}\text{'}}(x)>0y=-x+2y=f(x)xx-y=f(x)f(x)=x^a(b-x{)}^{c}a,$bca$=,b=,$ and $,c=6$

$(5)$ The line $y=-x+2is$ a slant asymptote $of$ the graph $ofy=f(x)$ both $asx$ and $asx-$

$a.$ Sketch the graph $ofy=f(x).$

$b.$ Fill $in$ the boxes $to$ make the following a true statement.

The function $f(x)=x^a(b-x{)}^c$ satisfies the conditions $(1)-(5)if$ the constants $a,b$ and $c$ are chosen $as$

$a=,b=,$ and $,c=4$ and $x6$

$(4)f^{\text{'}\text{'}}(x)<mn>0</mn>$ for $x<mn>6</mn>$ and $x0$;$f^{\text{'}\text{'}}(x)>0$ for $6$

$(5)$ The line $y=-x+2is$ a slant asymptote $of$ the graph $ofy=f(x)$ both $asx$ and $asx-$

$a.$ Sketch the graph $ofy=f(x).$

$b.$ Fill $in$ the boxes $to$ make the following a true statement.

The function $f(x)=x^a(b-x{)}^c$ satisfies the conditions $(1)-(5)if$ the constants $a,b$ and $c$ are chosen $as$

$a=,b=,$ and $,c=0$ for $4$ and $x6$

$(4)f^{\text{'}\text{'}}(x)<mn>0</mn>$ for $x<mn>6</mn>$ and $x0$;$f^{\text{'}\text{'}}(x)>0$ for $6$

$(5)$ The line $y=-x+2is$ a slant asymptote $of$ the graph $ofy=f(x)$ both $asx$ and $asx-$

$a.$ Sketch the graph $ofy=f(x).$

$b.$ Fill $in$ the boxes $to$ make the following a true statement.

The function $f(x)=x^a(b-x{)}^c$ satisfies the conditions $(1)-(5)if$ the constants $a,b$ and $c$ are chosen $as$

$a=,b=,$ and $,c=$