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Question
Find two positive numbers whose sum is 12 and their product is maximum
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Solution
Let the two numbers be x, 12 – x.
Their product p = x(12 – x) = 12x – x2
To find the maximum product.
p'(x) = 12 – 2x
p”(x) = – 2
p'(x) = 0
⇒ 12 – 2x = 0
⇒ 2x = 12
⇒ x = 6
At x = 6
p”(x) = – 2
= – ve
⇒ p is maximum at x = 6
when x = 6, 12 – x = 12 – 6 = 6
So the two numbers are 6, 6
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