students initially consider the value that 'c' should have for the area to be a maximum
they can then look at their three different area values
and possibly establish that the differences between the differences will always differ by 1
e.g. for 3 , 4 , 5
- smallest area = 13.5
- middle area = 16
- largest area = 17.5
16 - 13.5 = 2.5
the differences from the middle one are 1 apart
proving this relationship involves quadratic expansions
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