Answer
This statement makes sense.
Work Step by Step
Consider the given function $f\left( x \right)=c$ and the difference quotient formula $\frac{f\left( x+h \right)-f\left( x \right)}{h}$.
Substitute $x+h$ in place of x to find the value of $f\left( x+h \right)$.
In the given function, there is no term that consists of x, so after substitution, it will results in $f\left( x+h \right)=c$.
So,
$\begin{align}
& f\left( x+h \right)=c \\
& f\left( x \right)=c
\end{align}$
Substituting the values of $f\left( x \right)\text{ and }f\left( x+h \right)$ in the difference quotient formula
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{c-c}{h} \\
& =\frac{0}{h} \\
& =0
\end{align}$
Hence, the difference quotient formula always gives zero when $f\left( x \right)=c$.
Hence, the statement makes sense.
