Let P = V²R/(R + r)² as in Example 6. Calculate dP/dr, assuming that r is variable and R is constant.

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EXAMPLE 6 Power Delivered by a Battery The power that a battery supplies to an apparatus such as a laptop depends on the internal resistance of the battery. For a bat- tery of voltage V and internal resistance r, the total power delivered to an apparatus of resistance R (Figure 3) is V FIGURE 3 Apparatus of resistance R attached to a battery of voltage V. V²R (R+r)² (a) Calculate dP/dR, assuming that V and r are constants. (b) Where, in the graph of P versus R, is the tangent line horizontal? P =