AP Calculus BC / Unit 5: Analytical Applications of Differentiation
5.10 Introduction to Optimization Problems
Notes
Optimization means finding the largest or smallest value of a quantity. Write the quantity as a function of one variable, find its domain, and look for critical points and endpoints.
- Use a constraint equation to remove extra variables.
Practice
A rectangle has perimeter 20. Writing its area in terms of width $w$ gives:
Length is $10-w$.
The maximum area of that rectangle is:
$w=5$ gives a 5 by 5 square.
Why is the domain important in optimization?
A length can't be negative, for example.
Ready for more? Take the Unit 5 test.