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Question
You did a great job helping me with a previous question, hopefully you can do one more! Thanks!
*A home gardener estimates that 33 apple trees will have an average yield of 30 apples per tree. But because of the size of the garden, for each additional tree planted the yield will decrease by two apples per tree. How many trees should be planted to maximize the total yield of apples?
What is the maximum yield?
Let T = number of trees and let A = nummber of apples per tree.
Let x be the additional trees that are planted.
To get the total apples, multiply the number trees by the number of apples per tree. The problem is then maximize the equation
N(x)=(T+x)(A-x).
To do this problem, you can find the derivative by the product rule or multiply it out and find the derivative that way.
Either way, once the derivative is gotten, set it equal to 0 and solve.
To test and see if it is a true maximum, you can put in a value of x that is 1 more and 1 less than the value gotten or you can take the second derivative. Note that this problem involves a -x², so the second derivative is -2.
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Scotto
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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.
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I graduated with honors in both my BS and MS degree from Oregon State University.
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