A function $f$ that is twice$-$differentiable on the entire real line satisfies the following conditions:

$(1)f(0)=0,f(\sqrt[3]{2})=3\sqrt[3]{4},f(2)=8,f(\sqrt[3]{20})=0$

$(2)f^{\text{'}}(x)<mn>0</mn>$ for $x<mn>0</mn>$ and for $x>2$;$f^{\text{'}}(x)>0$ for $f^{\text{'}\text{'}}(x)>0x<mroot><mrow><mn>2</mn><mspace\; width="thinmathspace"></mspace></mrow><mrow><mn>3</mn></mrow></mroot>$;

$(3)f^{\text{'}\text{'}}(x)>0$ for $x<mroot><mrow><mn>2</mn><mspace\; width="thinmathspace"></mspace></mrow><mrow><mn>3</mn></mrow></mroot>$;$f^{\text{'}\text{'}}(x)<mn>0</mn>$ for $x>\sqrt[3]{2}$

$a.$ Sketch the graph $ofy=f(x)$ making sure that all important features are clearly shown.

b$.$ Fill in the boxes to make the following a true statement. The function $f(x)=a{x}^b+c{x}^d$ satisfies the conditions $(1,2,3$ if $a,b,c$ and $d$ are chosen as