Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)

Question

Mathematics

Barrett

16 February, 07:02

Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)

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Kolten Benton · Answer 1

4 and 4

Step-by-step explanation:

We have 2 numbers that will be X and Y

X * Y = 16 = > Y = 16 / X

We must minimize the sum, therefore:

S = X + Y

S = X + 16 / X

we derive and equal 0 and we are left with:

dS / dA = 1 - 16 / (X ^ 2) = 0

1 = 16 / X ^ 2

X ^ 2 = 16

X = 4

in the case of Y:

Y = 16/4 = 4

Therefore the numbers are 4 and 4.