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Find Two Positive Numbers X and Y Such that X + Y = 60 and Xy3 is Maximum. - CBSE (Commerce) Class 12 - Mathematics

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Question

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

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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 6: Application of Derivatives
Q: 14 | Page no. 233
Solution Find Two Positive Numbers X and Y Such that X + Y = 60 and Xy3 is Maximum. Concept: Maxima and Minima.
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