Answer
\[y = 11x - 6\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = \,\left( {2x - 1} \right)\,\left( {x + 4} \right) \hfill \\
Use\,\,the\,\,product\,\,rule\,\,to\,\,find\,\,{f^,}\,\left( x \right) \hfill \\
{f^,}\,\left( x \right) = \,\left( {2x - 1} \right)\,{\left( {x + 4} \right)^,} + \,\left( {x + 4} \right)\,{\left( {2x - 1} \right)^,} \hfill \\
Then \hfill \\
{f^,}\,\left( x \right) = \,\left( {2x - 1} \right)\,\left( 1 \right) + \,\left( {x + 4} \right)\,\left( 2 \right) \hfill \\
{f^,}\,\left( x \right) = 2x - 1 + 2x + 8 \hfill \\
{f^,}\,\left( x \right) = 4x + 7 \hfill \\
Evaluate\,\,{f^,}\,\left( x \right)\,\,at\,\,x = 1 \hfill \\
{f^,}\,\left( 1 \right) = 4\,\left( 1 \right) + 7 \hfill \\
{f^,}\,\left( 1 \right) = 11 \hfill \\
Then \hfill \\
m = 11 \hfill \\
Use\,\,y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\
y - 5 = 11\,\left( {x - 1} \right) \hfill \\
Simplifying \hfill \\
y - 5 = 11x - 11 \hfill \\
y = 11x - 6 \hfill \\
\hfill \\
\end{gathered} \]
