What is the simplified average rate of change What is the simplified average rate of change between $x = 3$ and $x = 3 + h$ for the function $f(x) = -x^2 + 5$?
I know you start off with $\frac{f(x+h)-f(x)}{h}$ but after substitution I got $-15+h+x^2$. What is the correct solution? 

$$
\begin{eqnarray}
\frac{f(x+h)-f(x)}{h} &=& \frac{(-(x+h)^2 + 5) - (-x^2 + 5)}{h} \\
&=& \frac{(-x^2 - 2xh - h^2 + 5) - (-x^2 + 5)}{h} \\
&=& \frac{-2xh - h^2}{h} \\
&=& -2x - h
\end{eqnarray}
$$
