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Find two positive numbers whose product is $ 100 $ and whose sum is a minimum.

$\begin{aligned} x &=10 \\ y &=10 \end{aligned}$

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Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

two numbers whose product? Just 100 pretty straightforward x times wise 100 and then acts plus y on them together gives us our minimum. Right? Okay, No, we know that we can write this as acts equals 100. Divided by why, Right? Because we're taking this first equation over here writing this simply in terms of X. Now we know writing this in terms of a singular variable 100 over Why Post, why is our minimum take? The derivative derivative of Y is simply one said equal to zero because we know the minimum value would be like the constant we end up with. Why is ton therefore X is also 10 times 10 times 10 is 100.