Answer
The difference quotient for the given function is $6$
Work Step by Step
$f(x)=6x+1$
Find the difference quotient $\dfrac{f(x+h)-f(x)}{h}$
Start by finding $f(x+h)$. Substitute $x$ by $x+h$ in $f(x)$ and simplify:
$f(x+h)=6(x+h)+1=6x+6h+1$
Substitute the known values into the formula for the difference quotient and simplify:
$\dfrac{f(x+h)-f(x)}{h}=\dfrac{6x+6h+1-(6x+1)}{h}=...$
$...=\dfrac{6x+6h+1-6x-1}{h}=\dfrac{6h}{h}=6$
The difference quotient for the given function is $6$
