Q. 134.3( 46 Votes )
Find two numbers
Let one number be x. Then, the other number is (24 –x).
Let P(x) denote the product of the two numbers.
Then, we get,
P(x) = x(24 –x) = 24x – x2
⇒ P’(x) = 24 – 2x
⇒ P’’(x) = -2
Now, P’(x) = 0
⇒ x = 12
P’’(12) = -2 <0
Then, by second derivative test,
x = 12 is the point of local maxima of P.
Therefore, the product of the numbers is the maximum when the numbers are 12 and 24 – 12 = 12.
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