Explain Please?
if #x+y=4# for positive integers
x and y , then the smallest possible value of #1/x + 1/y #
if
x and y , then the smallest possible value of
3 Answers
1
Explanation:
There are only two possible combinations of positive integer
Let
Let
Therefore, since
Isn't it 1
Explanation:
Substituting in the equation:
LCM of denominators is
Combining the denominators:
Given:
Minimize:
Substitute
Compute the first derivative with respect to x:
To find local extrema we set the first derivative equal to 0:
Multiply both sides by
Expand the square:
Find the corresponding value of y:
The value is:
We could perform the second derivative test but we know that this is a minimum because it is obvious that the maximum occurs when either