Maxima and Minima

An orange grove now has 40 trees per acre with an average yield of 1000 oranges per tree.  It is observed that for each additional tree planted per acre, the yield per tree is reduced by 20 oranges.  What is the maximum yield per acre that the grove will produce?  Make careful arguments that show you indeed have the maximum value.

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 2: Question 13, p. 11)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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