501 Calculus Questions by LLC LearningExpress

Author:LLC LearningExpress [LearningExpress, LLC]
Language: eng
Format: epub
ISBN: 111-1-11-111111-1

Since the sign of Price′(x) changes from + to – at x = 25, we conclude that Price(x) has a local maximum at x = 25. Thus, the watermelons will fetch the highest price possible in 25 days.

272. The area is Area = xy. Also, by adding the lengths of all sides for which fencing will be used, we see that the total fencing is 4y + 2x = 400. Thus, x = 200 – 2y, so the area function can be written as Area (y) = xy =(200 – 2y)y = 200y – 2y2

Applying the first derivative test requires that we compute the first derivative, as follows: Area ′(y) = 200 – 4y

Observe that Area ′(y) is defined at all real numbers, and the only y-value that makes it equal zero is y = 50. To assess how the sign of Area′(y) changes, we form a number line using the critical points, choose a value in each subinterval, and report the sign of Area′(y) above the subinterval, as follows:

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