Calculus Section 4.4
Page 20
4.4
Modeling and Optimization
(Extreme Value Problems)
Method for solving extreme value problems
Step 1
. Draw an appropriate figure and label the quantities relevant to the problem.
Step 2
. Find a formula for the quantity to be maximized or minimized.
This is called
developing a
“mathematical model”
for the problem.
Step 3.
Using the conditions stated in the problem to eliminate variables, express the
quantity to be maximized or minimized as a function of one variable.
Step 4.
Find the interval of possible values for this variable from the physical restrictions
in the problem.
(This can be done using the graph of the function.)
Step 5.
Use techniques to obtain the maximum or minimum (use calculus to identify the
critical points and endpoints – can always use the graph to verify )
Example 1
Find two numbers whose sum is 20 and whose product is as large as possible.
Example 2.
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 Spring '10
 John
 Calculus, Calculus Section, extreme value problems

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