#### Answer

\[{f^{,,}}\,\left( 0 \right) = \,16\,\,\,\,\,and\,\,\,\,{f^{,,}}\,\left( 2 \right) = 16\]

#### Work Step by Step

\[\begin{gathered}
f\,\left( x \right) = 8{x^2} + 6x + 5 \hfill \\
Find\,\,the\,\,derivative\,\,of\,\,the\,\,function \hfill \\
{f^,}\,\left( x \right) = \,\,{\left[ {8{x^2} + 6x + 5} \right]^,} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
{f^,}\,\left( x \right) = 16{x^{2 - 1}} + 6\,\left( 1 \right) \hfill \\
{f^,}\,\left( x \right) = 16x + 6 \hfill \\
Find\,\,the\,\,\sec ond\,\,derivative \hfill \\
{f^{,,}}\,\left( x \right) = \,\,{\left[ {16x + 6} \right]^,} \hfill \\
{f^{,,}}\,\left( x \right) = 16 \hfill \\
Then \hfill \\
{f^{,,}}\,\left( 0 \right) = \,16\,\,\,\,\,and\,\,\,\,{f^{,,}}\,\left( 2 \right) = 16 \hfill \\
\end{gathered} \]