Two numbers have a sum of $24$. Their product is largest when the numb…

Question

Two numbers have a sum of $24$. Their product is largest when the numbers are

Accepted Answer

C. $12$ and $12$

1. Let the numbers be $x$ and $24-x$; product $P=x(24-x)=24x-x^2$.
2. $P'(x)=24-2x=0 \Rightarrow x=12$.
3. $P''(x)=-2<0$, so $x=12$ gives the maximum.
4. The numbers are $12$ and $24-12=12$.
_Source: syllabus Mathematics Ch 6 "Application of Derivatives", p.29_

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Two numbers have a sum of $24$. Their product is largest when the numbers are

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