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?

Verified step by step guidance

1. Step 1: Understand that the rate of change of the charge Q with respect to time is represented by the derivative Q'(t). We are looking for the time at which this derivative is the greatest.
2. Step 2: Analyze the graph of Q(t) provided in the image. The rate of change, Q'(t), is represented by the slope of the tangent line to the curve at any point.
3. Step 3: Identify the point on the graph where the slope of the tangent line is steepest. This point corresponds to the maximum value of Q'(t).
4. Step 4: If the graph is not available, consider the mathematical function Q(t) if provided. Take the derivative of Q(t) to find Q'(t) and determine where this derivative reaches its maximum value.
5. Step 5: Verify the time at which Q'(t) is greatest by checking the concavity of Q(t) around this point, ensuring it is indeed a maximum.