Calculate the Average Rate of Change of the Given Function $[ a , a + h ]$

Multiple Choice

Calculate the average rate of change of the given function f over the interval $[ a , a + h ]$ , where $h = 1,0.1,0.01,0.001$ , and $0.0001$ . (It will be easier to do this if you first simplify the difference quotient (dq) as much as possible.) $f ( x ) = 5 x ^ { 2 } ; a = 0$ Complete the table. $$\begin{array} { | c | c | } \hline \boldsymbol { h } & d q \\\hline 1 & \\\hline 0.1 & \\\hline 0.01 & \\\hline 0.001 & \\\hline 0.0001 & \\\hline\end{array}$$

A) $\begin{array} { l } d q \\5 \\0.05 \\0.0005 \\0.000005 \\0.00000005\end{array}$

B) $\begin{array} { l } d q \\5 \\0.5 \\0.05 \\0.000001 \\0.0001\end{array}$

C) $\begin{array} { l } d q \\6 \\5.1 \\5.01 \\5.001 \\5.0001\end{array}$

D) $\begin{array} { l } d q \\5 \\0.5 \\0.05 \\0.005 \\0.0005\end{array}$