Question

divide 100 into 2 parts such that their product is maximum​

Answer 1

Answer:

the number are 50 and 50

Step-by-step explanation:

product =50*50=2500 max

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Answer 2

Given:

Number 100

To Find:

Part of 100 such that their product is maximum.

Solution:

Let one part of 100 be x,

then another part will be (100 - x)

⇒ Product = x . (100 - x)

                  = 100x - x²

now let f(x) = 100x - x²

f'(x) = 100 - 2x

f'(x) = 0 will be point of maximum or minimum value

⇒ 100 -2x = 0

⇒ 2x = 100

⇒ x = 50

f"(x) = -2

as f"(x) is negative for every value of x so at x = 50 f(x) will be maximum.

so one part will x and another part (100 - x) = 50

product = 50 × 50 = 2500

Hece , product is maximun when part of 100 are 50 and 50.