Answer
\[\,\,\,\,\,\,\,\,\,\,\, = - 14\,\,,\,\,46\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = 5{x^3} - 7{x^2} + 4x + 3 \hfill \\
Find\,\,{f^{,\,}}\,\left( x \right)\,\,for\,\,the\,\,function \hfill \\
{f^,}\,\left( x \right) = \,{\left( {5{x^3} - 7{x^2} + 4x + 3} \right)^,} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\frac{d}{{dx}}\,\,\left[ {{x^n}} \right] = n{x^{n - 1}} \hfill \\
{f^,}\,\left( x \right) = 15{x^2} - 14x + 4 \hfill \\
and \hfill \\
{f^{,,}}\,\left( x \right) = \,{\left( {15{x^2} - 14x + 4} \right)^,} \hfill \\
{f^{,,}}\,\left( x \right) = 30x - 14 \hfill \\
find\,\,{f^{,,}}\,\left( 0 \right)\,\,and\,{f^{,,}}\,\left( 2 \right)\,\, \hfill \\
{f^{,,}}\,\left( 0 \right) = 30\,\left( 0 \right) - 14 = - 14 \hfill \\
{f^{,,}}\,\left( 2 \right) = 30\,\left( 2 \right) - 14 = 46 \hfill \\
\end{gathered} \]
