Approximate rate of change from graphs and tables of values

Practice Questions

AP Calculus AB › Approximate rate of change from graphs and tables of values

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$\begin{align*}&x&f(x)\&3&27\&8&8\&13&43\&18&8\&23&-49\&28&-38\&33&37\&\text{Approximate a backward derivative at }x=33\end{align*}$

$\begin{align*}&t&p(t)\&2&24\&3&6\&4&-32\&5&10\&6&-20\&7&-37\&8&-29\&9&40\&\text{The above table lists a particle's postion at different times.}\&\text{Approximate its velocity with a forward difference at }t=2\end{align*}$

$\begin{align*}&\text{Approximate a forward derivative at }x=4\&\text{Using the following table:}\&x&&f(x)\&1&&5\&4&&-8\&7&&15\end{align*}$

$\begin{align*}&\text{Approximate the acceleration of a particle using}\&\text{a central difference approach at }t=6\&\text{Using the following table of positions:}\&t&p(t)\&2&26\&6&-23\&10&18\&14&16\&18&-34\end{align*}$

$\begin{align*}&x&f(x)\&-3&12\&1&-14\&5&-45\&9&-1\&13&-31\&17&-38\&\text{Approximate a backward derivative at }x=1\end{align*}$

$\begin{align*}&t&p(t)\&3&-31\&4&-41\&5&-19\&6&-4\&7&-40\&\text{The above table lists a particle's postion at different times.}\&\text{Approximate its velocity with a forward difference at }t=6\end{align*}$

$\begin{align*}&t&p(t)\&2&-28\&4&25\&6&-25\&8&1\&10&20\&12&39\&14&46\&16&5\&\text{The table above lists the positions of a particle}\&\text{At various times. Approximate the acceleration at }t=4\&\text{Using a central difference approach.}\end{align*}$

$\begin{align*}&x&f(x)\&1&-27\&3&-38\&5&11\&7&-5\&9&-4\&11&16\&13&27\&15&-15\&\text{Using the above table, make a forward derivative approximation at }x=9\end{align*}$

$\begin{align*}&t&p(t)\&1&32\&6&-26\&11&43\&16&-15\&\text{The table above lists the positions of a particle}\&\text{At various times. Approximate the acceleration at }t=6\&\text{Using a central difference approach.}\end{align*}$

$\begin{align*}&t&p(t)\&0&33\&3&-16\&6&-21\&9&25\&12&-49\&15&-46\&18&17\&21&10\&\text{Using the above table of positions,}\&\text{make a forward difference velocity approximation at }t=9\end{align*}$

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