Weighing my Balance
You can place weights on both side of weighing balance and you need to measure all weights between 1 and 1000. For example if you have weights 1 and 3,now you can measure 1,3 and 4 like earlier case, and also you can measure 2,by placing 3 on one side and 1 on the side which contain the substance to be weighed. So question again is how many minimum weights and of what denominations you need to measure all weights from 1kg to 1000kg.
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1 solution
For the local min and max, f'(x) will be zero at f(-1) and f(1)
3a - 2b + c = 0 and 3a + 2b + c = 0...............from these, b must = zero
f(x) = ax^3 + cx + d
f(1) = a + c + d = -1 f(-1) = -a -c + d = 2...........add these two, and 2d = 1...........d = 1/2
Now we have 3a + c = 0 and .................. a + c = -3/2
2a = 3/2...............a = 3/4...............c = - 9/4