2. Intro to Derivatives

Based on the graph of $f\left(x\right)$, describe the graph of the derivative $f^{\prime}\left(x\right)$ on the interval $\left(0,\infty\right)$.

Based on the graph of $f\left(x\right)$, describe the graph of the derivative $f^{\prime}\left(x\right)$at the point $x=-1$.

Based on the graph of $f\left(x\right)$, describe where the derivative curve $f^{\prime}\left(x\right)$ would be below the x-axis.

Based on the graph $f\left(x\right)$, describe all points where the derivative $f^{\prime}\left(x\right)$would have a jump.

Reproduce the graph of f and then plot a graph of f' on the same axes. <IMAGE>

A capacitor is a device in an electrical circuit that stores charge. In one particular circuit, the charge on the capacitor Q varies in time as shown in the figure. <IMAGE>

a. At what time is the rate of change of the charge Q' the greatest?

A capacitor is a device in an electrical circuit that stores charge. In one particular circuit, the charge on the capacitor Q varies in time as shown in the figure. <IMAGE>

b. Is Q′ positive or negative for t≥0?

Where is the function continuous? Differentiable? Use the graph of f in the figure to do the following. <IMAGE>

c. Sketch a graph of f'.