Slope of a curve at a point

Practice Questions

AP Calculus AB › Slope of a curve at a point

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

Find the slope of the curve, , at .

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

Find the normal line to the function $f(x)=\frac{4}{x}$ at the point .

Find the slope of the line tangent to the curve of f(x) when . Round to the nearest whole number.

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$\begin{align*}&\text{Determine the sign of the derivative of the function above at the point }\&x=2\end{align*}$

Find the rate of change of f(x) at the point (4,12).

$\begin{align*}&\text{Calculate the slope of the function:}\&f(x)=4x + cos(8\cdot \pi x) - sin(\frac{(13\cdot \pi x)}{2}) + 2x^{2} + 3\&\text{At the point }x=2\end{align*}$

Find the slope of the curve , at .

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$\begin{align*}&\text{Determine whether or not the derivative of the function above at the point }\&x=7\&\text{is positive, negative, or zero.}\end{align*}$

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