1. The problem statement, all variables and given/known data attached 2. Relevant equations 3. The attempt at a solution First I decided to find the equivalent resistance. Since r2 and r3 are parallel, this can be combined into a resistor of resistance r2r3/(r2 + r3). Since r2 is known, I went ahead and wrote that as 14r3/(14+r3). Now, this resistor is in series with r1, so I can find the equivalent resistance to be 2 + [14r3/(14+r3)] Now, I can call the current due to the battery i = V/R = V/(2 + [14r3/(14+r3)]) Allowing me to use the dissipation formula for r3 P = r3[V/(2 + [14r3/(14+r3)])]^2 Now I figured it would be a matter of differentiating this function and setting it equal to zero, but the derivative is unreasonably complex. Any ideas?