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monroe17
 3 years ago
find two numbers a and b (with a≤b) whose difference is 38 and whose product is minimized
monroe17
 3 years ago
find two numbers a and b (with a≤b) whose difference is 38 and whose product is minimized

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1if one number is \(x\) and the other is \(y\) then their difference is \(xy=38\) making \(y=x38\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1you want to minimize the product \[x(x38)=x^238x\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1minimum will be at the vertex \(\frac{b}{2a}=\frac{38}{2}=19\)

carson889
 3 years ago
Best ResponseYou've already chosen the best response.0Or it can be found by finding the critical point. That is, where the derivative of the above found product is equal to zero. So the derivative of \[x ^{2} 38x\] is \[2x  38\], set it equal to zero and solve for x, x = 19.

monroe17
 3 years ago
Best ResponseYou've already chosen the best response.0got it! 19 and 19 (: thanks!
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