According to a certain estimate, the depth N(t), in centimeters, of the water in a certain tank at t hours past 2:00 in the morning is given by N(t)= -20(t-5)^²+500 for 0≤t≤10. According to this estimate, at what time in the morning does the depth of the water in the tank reach its maximum?
Don't get bogged down by the dirty N(t) expression. Just think of it this way:
N(t) is a combination of two terms: a positive term (500) and a negative term (\(-20(t-5)^2\)).
To maximize N(t), I need to make the positive term as large as possible (It is a constant here so I cannot do much with it) and the absolute value of the negative term as small as possible. The smallest absolute value is 0. Can I make it 0? Yes, if I make t = 5, the negative term becomes 0 and N(t) is maximized. My answer must be 2:00 + 5 hrs i.e. 7:00.
Most of the maximum minimum questions on GMAT will require you to only think logically. The calculations involved will be minimum.
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