Question

Find two numbers whose sum is 8 and whose product is a maximum in application of derivative

Answer 1

Given : Two numbers sum is 8 and   product is a maximum  

To Find : Two numbers

Solution:

Two numbers sum is 8

One number is x

Then other number is  8 - x

Product = x(8 - x)

P(x)  = 8x - x²

Taking derivative

P'(x) = 8 - 2x

 P'(x) = 0

8 - 2x = 0

=> x = 4

p''(x) = - 2  < 0

Hence product is maximum at x = 4

x = 4  => 8 - x = 4

Hence both the numbers are  4 and 4

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