Find two positive numbers whose product is 190 and whose sum is a minimum.
D)1, 190
E)0, 190

Question

Find two positive numbers whose product is 190 and whose sum is a minimum.
D)1, 190 
E)0, 190

Quizplus · Accepted Answer

Let the two positive numbers be $x$ and $y$. We want to minimize $x+y$ subject to the constraint $xy=190$. This means we can write $y=\frac{190}{x}$ and we want to minimize $x+\frac{190}{x}$. We can find the minimum of this function by taking the derivative and setting it equal to zero: $$\frac{d}{dx}\left(x+\frac{190}{x}ight) = 1-\frac{190}{x^2}=0.$$ Solving for $x$, we get $x=\sqrt{190}$, which means $y=\frac{190}{\sqrt{190}}=\sqrt{190}$. Therefore, the two positive numbers that minimize the sum are $\sqrt{190}$ and $\sqrt{190}$, which add up to $2\sqrt{190}$. The answer is $\boxed{	extbf{(C) }11ec1854_fdb7_993b_acfc_d1ac8ea7dbc1\_TBX8702\_11}$.

Find Two Positive Numbers Whose Product Is 190 and Whose