Question

If $x+y=10$ , then the maximum value of $xy$ is

• A. $5$
• B. $20$
• C. $25$
• D. None of these

Answer 1

Answer: (C)

Given, $x+y=10$ $y=10-x$ ... (i)
Now, $f(x)=xy=x(10-x)=10x-x^2$
$\therefore$ $f^{\prime }(x)=10-2x$
For maximum value of $f(x)$ , put $f^{\prime }(x)=0$
$\Rightarrow$ $10-2x=0\Rightarrow x=5$
$\therefore$ $x=5$ and $y=5$ [from Eq. (i)]
Hence, maximum value of $xy=5\times 5=25$