The two numbers with a difference of 62 and whose product is a minimum are; 31 and -31
- Let the two numbers be x and y.
We are told that their difference is 62.
Thus; x - y = 62 ---(1)
- We want their products to be minimum. Thus;
f(x,y) = xy
From eq, making y the subject gives us;
y = x - 62
Thus;
f(x) = x(x - 62)
f(x) = x² - 62x
- For the product to be minimum, let us find the derivative of f(x) and equate to zero. Thus;
f'(x) = 2x - 62
At f'(x) = 0
2x - 62 = 0
2x = 62
x = 62/2
x = 31
Thus;
y = 31 - 62
y = -31
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