Question

Find the maximum or minimum value of the product of two numbers whose difference is 14.49343-56-49

Answer 1

Given:

The difference between the two numbers is 14.

Required:

We need to find the maximum or minimum value of the product of two numbers whose difference is 14.

Step-by-step explanation:

Let x be the first number.

The difference between the two numbers is 14.

The second number is x-14.

The product of the two numbers is

`x(x-14)`
`x^2-14x`

Differentiate this with respect to x and equate it to zero.

`2x-14=0`
`2x-14+14=0+14`
`2x=14`

Divide both sides by 2.

`(2x)/(2)=(14)/(2)`
`x=7`

Substitute x =7 in the product.

`(7)^2-14(7)=-49`

Final answer:

The maximum or minimum value of the product of two numbers whose difference is 14 is -49.