Divide the number 20 into two parts such that their product is maximum - Mathematics and Statistics

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Sum

Divide the number 20 into two parts such that their product is maximum

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Solution

The given number is 20.

Let x be one part of the number and y be the other part.

∴ x + y = 20

∴ y = (20 – x)      ......(i)

The product of two numbers is xy.

∴ f(x) = xy

= x(20 – x)    ......[From (i)]

= 20x – x2

∴ f'(x) = 20 – 2x and f''(x) = – 2

Consider, f'(x) = 0

∴ 20 – 2x = 0

∴ 20 = 2x

∴ x = 10

For x = 10,

f''(10) = – 2 < 0

∴ f(x), i.e., product is maximum at x = 10

and y = 20 – 10     ......[From (i)]

i.e., y = 10

  Is there an error in this question or solution?
Chapter 1.4: Applications of Derivatives - Q.4

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