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AP Calculus AB · Unit 5: Analytical Applications of Differentiation
5.10 Introduction to Optimization
What it is
Optimization finds the maximum or minimum of a quantity, subject to a constraint. The quantity being optimized is the objective function.
The approach
Use the constraint to write the objective in one variable, then apply calculus — find critical points — to locate the extremum.
Key terms
- Optimization
- Finding a maximum or minimum subject to a constraint.
- Objective function
- The quantity being maximized or minimized.
- Constraint
- An equation used to reduce to one variable.
- Method
- Find critical points of the objective.
- Goal
- Locate the extreme value.
Try an AP-style question
Two positive numbers have a sum of 20. What is their largest possible product?
- 96
- 20
- 100
- 400
Show the answer
C. P = x(20 − x); P' = 20 − 2x = 0 → x = 10; 10 · 10 = 100.
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