Answer
\[ = 4x + 2h - 3\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = 2{x^2} - 3x + 1 \hfill \\
\hfill \\
Use{\text{ }}the{\text{ }}definition{\text{ }}of{\text{ }}derivative \hfill \\
\hfill \\
\frac{{f\,\left( {x + h} \right) - f\,\left( x \right)}}{h} = \frac{{2\,{{\left( {x + h} \right)}^2} - 3\,\left( {x + h} \right) + 1 - 2{x^2} + 3x - 1}}{h} \hfill \\
\hfill \\
multiply \hfill \\
\hfill \\
= \frac{{2{x^2} + 4xh + 2{h^2} - 3x - 3h + 1 - 2{x^2} + 3x - 1}}{h} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
= \frac{{4xh + 2{h^2} - 3h}}{h} \hfill \\
\hfill \\
= \frac{{h\,\left( {4x + 2h - 3} \right)}}{h} \hfill \\
\hfill \\
= 4x + 2h - 3 \hfill \\
\end{gathered} \]
