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
[tex]x(x-14)[/tex][tex]x^2-14x[/tex]Differentiate this with respect to x and equate it to zero.
[tex]2x-14=0[/tex][tex]2x-14+14=0+14[/tex][tex]2x=14[/tex]Divide both sides by 2.
[tex]\frac{2x}{2}=\frac{14}{2}[/tex][tex]x=7[/tex]Substitute x =7 in the product.
[tex](7)^2-14(7)=-49[/tex]Final answer:
The maximum or minimum value of the product of two numbers whose difference is 14 is -49.
