An equilateral triangle ΔLMQ (see picture to the right) is drawn in the interior of square LMNP so that side LM is common. Find
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There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
