Maximum power is the steepest slope on the energy-time graph

Steps:

• Instantaneous power equals the derivative of energy with respect to time: P = dE/dt.
• Plot energy E versus time t; the slope at any point is the power at that instant.
• Examine the graph to find the segment with the maximum slope.
• Compute that slope: rise over run yields 30 J/s, or 30 W.

Why C is correct:

• Power is defined as the time rate of change of energy (P = dE/dt), so the graph's steepest slope of 30 units/second gives the peak power of 30 W.

Why the others are wrong:

• A. 10W: Corresponds to a gentler initial slope, not the maximum.
• B. 13W: Reflects an average or lesser slope, below the peak.
• D. 50W: Overestimates; no slope in the graph reaches this value.

Final answer: C