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Find Two Numbers Whose Sum is 24 and Whose Product is as Large as Possible. - Mathematics

Find two numbers whose sum is 24 and whose product is as large as possible.

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Solution

Let one number be x. Then, the other number is (24 − x).

Let P(x) denote the product of the two numbers. Thus, we have:

∴By second derivative test, x = 12 is the point of local maxima of P. Hence, the product of the numbers is the maximum when the numbers are 12 and 24 − 12 = 12

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APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 13 | Page 233
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