Odd.................................
Yep!
Weighing #1: Start off by splitting the pile of 12 coins evenly into two piles, 6 in each pile. Put one pile on each side of the balance. The side that is weighed down has the fake coin it in. Ignore the other 6 coins.
Weighing #2: Now you have 6 coins left. Split the pile evenly again, 3 in each pile. Repeat the same process and put each pile on one side of the balance. The side that is weighed down has your fake coin in it. Ignore the other 3 coins.
Weighing #3: You have 3 coins left. Take two coins, whichever two you like, and weigh them. If they weigh the same, then the one you didn't weigh is the fake one. If one is heavier, then that heavier one is your fake coin.
To get the extrema, derive the function.
You get y' = 2x^-1/3 - 2.
Set this equal to zero, and you get x=0 as the location of a critical point.
Since you are on a closed interval [-1, 1], those points can also have an extrema.
Your min is right, but the max isn't at (1,1). At x=-1, you get y=5 (y = 3(-1)^2/3 -2(-1); (-1)^2/3 = 1, not -1).
Thus, the maximum is at (-1, 5).
First of all, to simplify a number/fraction, you must find a common multiple.
Both 12 and 42 is divisible by 6
=
since 6 goes into 12, two times and goes into 42, 7 times. The answer is
when simplified.
