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-5i^2 + 120 i = P     will be max at   i = -b/2a      where a = -5    b = 120

          max will be   at   i =  -120 / (2* (-5)) = 12 amps

Another way to get the answer:

 

To find the maximum, find the first derivative and set it equal to zero.

 

Problem:             P  =  120·i  -  5·i²

 

First derivative:  P'  =  120  -  10i

 

Setting the first derivative to zero:  120  -  10·i  =  0

                                                                  -10·i  =  -120

                                                                        i  =  12 amps