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Find Two Positive Numbers X and Y Such that X + Y = 60 and Xy3 is Maximum. - Mathematics

Find two positive numbers x and y such that x + y = 60 and xy3 is maximum.

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Solution

The two numbers are x and y such that x + y = 60.

⇒ y = 60 − x

Let f(x) = xy3.

∴By second derivative test, = 15 is a point of local maxima of f. Thus, function xy3 is maximum when x = 15 and y = 60 − 15 = 45.

Hence, the required numbers are 15 and 45.

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APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 14 | Page 233
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