Answer
See explanation.
Work Step by Step
\begin{array}{l}
\lim _{h \rightarrow 0} \frac{f(h+x)-f(x)}{h} =f(x)\\
=\lim _{h \rightarrow 0} \frac{\left[3(x+h)^{2}+2(x+h)+1\right]-\left(3 x^{2}+2 x+1\right)}{h} \\
=\lim _{h \rightarrow 0} \frac{\left(3 x^{2}+6 x h+3 h^{2}+2 x+2 h+1\right)-\left(3 x^{2}+2 x+1\right)}{h} \\
=\lim _{h \rightarrow 0} \frac{6 x h+3 h^{2}+2 h}{h}=\lim _{h \rightarrow 0} \frac{h(6 x+3 h+2)}{h} \frac{f(x)}{h \rightarrow 0} \frac{\mid i m}{h \rightarrow 0}(6 x+3 h+2)=6 x+2 \\
=\lim _{h \rightarrow 0} \frac{[6(x+h)+2]-(6 x+2)}{h} \\
=\lim _{h \rightarrow 0} \frac{[6 x+6 h+2]-(6 x+2)}{h} \\
=\lim _{h \rightarrow 0} \frac{6 h}{h}=\lim _{h \rightarrow 0} 6=6
\end{array}