Exercise · ZW-OPTIMIZATION-PROBLEMS-007 · ★★☆ Intermediate
Two positive numbers add up to 20. What is the largest possible value of their product?
Choose one option.
Show answer
- C. \(100\)
Explanation
If the numbers are x and 20-x, the product is \(P(x)=x(20-x)\). \(P'(x)=20-2x=0\) gives x = 10, and the maximum product is \(P(10)=100\).
Review the concept: Optimization problems
An optimization problem seeks the largest or smallest value of a quantity subject to constraints, expressed as a function of one variable.
\[\text{maximize }A(x)\ \Rightarrow\ A'(x)=0\]
More practice problems: optimization problems
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- ZW-OPTIMIZATION-PROBLEMS-008 What is the minimum value of f(x)=x^2-6x+13?
- ZW-OPTIMIZATION-PROBLEMS-009 What is a critical point of a function f?
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