Exercise · ZW-OPTIMIZATION-PROBLEMS-003 · ★★☆ Intermediate
Two positive numbers have product 36. What is the smallest possible value of their sum?
Choose one option.
Show answer
- C. \(12\)
Explanation
If the numbers are x and 36/x, the sum is \(S(x)=x+\dfrac{36}{x}\). \(S'(x)=1-\dfrac{36}{x^{2}}=0\) gives x = 6, and the minimum sum is \(S(6)=6+6=12\).
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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