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Two positive numbers have product 13 Using calculus find the smallest possible value of their sum?
Wiki User
∙ 14y ago
Let x and y be positive numbers such that xy=13. Thus, y=13/x. We want to minimize t=x+y=x+13/x. Differentiate t=x+13/x.
t'=1-13x-2
Set this equal to zero.
1-13x-2=0
13x-2=1
x2=13
x=sqrt(13)
Now solve for y:
y=13/x=13/sqrt(13)=sqrt(13)
Wiki User
∙ 14y ago
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