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.

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.

$\frac{2x}{2}=\frac{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.