Applications of Derivatives · Applied Problems
Optimization
Optimization finds the maximum or minimum value of a function. Set up the objective function, find critical points, and test them.
- 0 variables
- 2 worked examples
- 15 in Applications of Derivatives
Worked examples
Find two positive numbers whose sum is 20 and whose product is maximum.
- Let x + y = 20, maximize P = xy = x(20-x) = 20x - x²
- P'(x) = 20 - 2x = 0 → x = 10
- P''(x) = -2 < 0 → local max ✓
Answer: x = y = 10, maximum product = 100.
1 more worked examplePremium
A rectangular pen is built against a straight wall using 100 m of fence on the other three sides. Find the dimensions that maximize its area.
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Practice
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