Exercise · ZW-OPTIMIZATION-PROBLEMS-010 · ★★☆ Intermediate
Maximize \(A(x)=x(10-x)\) on the interval \([0,4]\). What is the maximum value?
Choose one option.
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- D. \(24\)
Explanation
The critical point \(x=5\) lies outside \([0,4]\), so compare the endpoints: \(A(0)=0\) and \(A(4)=24\). The maximum is \(24\).
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.
\[\text{maximize }A(x)\ \Rightarrow\ A'(x)=0\]
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