#### Answer

\[\,\,\,\,\,\,\,\,\,\,\,\, - 4,152\]

#### Work Step by Step

\[\begin{gathered}
f\,\left( x \right) = 4{x^4} - 3{x^3} - 2{x^2} + 6 \hfill \\
Find\,\,{f^{,\,}}\,\left( x \right)\,\,for\,\,the\,\,function \hfill \\
{f^,}\,\left( x \right) = \,\,{\left[ {4{x^4} - 3{x^3} - 2{x^2} + 6} \right]^,} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
{f^,}\,\left( x \right) = 16{x^3} - 9{x^2} - 4x \hfill \\
Find\,\,{f^{\,,,}}\,\left( x \right) \hfill \\
{f^{\,,,}}\,\left( x \right) = \,{\left( {16{x^3} - 9{x^2} - 4x} \right)^,} \hfill \\
{f^{\,,,}}\,\left( x \right) = 48{x^2} - 18x - 4 \hfill \\
find\,\,{f^{,,}}\,\left( 0 \right)\,\,and\,{f^{,,}}\,\left( 2 \right)\,\, \hfill \\
{f^{\,,,}}\,\left( 0 \right) = 48\,{\left( 0 \right)^2} - 18\,\left( 0 \right) - 4 = - 4 \hfill \\
{f^{\,,,}}\,\left( 2 \right) = 48\,{\left( 2 \right)^2} - 18\,\left( 2 \right) - 4 = 152 \hfill \\
\hfill \\
\end{gathered} \]