#### Answer

\[\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10,58\]

#### Work Step by Step

\[\begin{gathered}
f\,\left( x \right) = 4{x^3} + 5{x^2} + 6x - 7 \hfill \\
Find\,\,{f^{,\,}}\,\left( x \right)\,\,for\,\,the\,\,function \hfill \\
{f^,}\,\left( x \right) = \,{\left( {4{x^3} + 5{x^2} + 6x - 7} \right)^,} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\
{f^,}\,\left( x \right) = 4\,\left( 3 \right){x^{3 - 1}} + 5\,\left( 2 \right){x^{2 - 1}} + 6\,\left( 1 \right) \hfill \\
{f^,}\,\left( x \right) = 12{x^2} + 10x + 6 \hfill \\
and \hfill \\
{f^{,,}}\,\left( x \right) = \,{\left( {12{x^2} + 10x + 6} \right)^,} \hfill \\
{f^{,,}}\,\left( x \right) = 24x + 10 \hfill \\
find\,\,{f^{,,}}\,\left( 0 \right)\,\,and\,{f^{,,}}\,\left( 2 \right)\,\, \hfill \\
{f^{,,}}\,\left( 0 \right) = 24\,\left( 0 \right) + 10 = 10 \hfill \\
{f^{,,}}\,\left( 2 \right) = 24\,\left( 2 \right) + 10 = 58 \hfill \\
\end{gathered} \]