Derivative at a point

Practice Questions

AP Calculus AB › Derivative at a point

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

Functionplot

$\begin{align*}&\text{Determine whether or not the derivative of the function above at the point }\&x=-1\&\text{is positive, negative, or zero.}\end{align*}$

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

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

Find the minimum value of $f(x)=\frac{1}{\sqrt{9-x^2}}$

Give the equation of the line tangent to the graph of the equation

$f(x) = 4x+ e^{x-2}$

at the point .

Find the slope of the curve, , at .

$\begin{align*}&\text{For positive values of x: }\&f(x)=cos(\frac{(\pi x)}{2}) - 5x + sin(4\cdot \pi x) - 5\&\text{Calculate the slope of the function at }x=6\end{align*}$

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

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

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