Answer
The difference quotient for the provided function is $6$.
Work Step by Step
a
Consider the provided function: $f\left( x \right)=6x+1$.
Now, substitute $x=x+h$ in the above equation to find $f\left( x+h \right)$
That is,
$f\left( x+h \right)=6\left( x+h \right)+1$
Now, apply the difference quotient formula,
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{6\left( x+h \right)+1-\left( 6x+1 \right)}{h} \\
& =\frac{6x+6h+1-6x-1}{h} \\
& =\frac{6h}{h} \\
& =6
\end{align}$
Hence, the difference quotient for the provided function is $6$.
