One number is 10 less than a second number. Find a pair of such number that their product is as small as possible.

Question

These two numbers are______

The smallest possible product is_____

Answer 1

Two numbers x and y

x+10=y

xy=x(x+10)

Now you need to mimize the function f(x)=x(x+10)

f'(x)=2x+10 --->, x=-5 is expreme point f''(-5)=2>0 --> x=-5 is minimum

f(-5)=-5*5=-25

x=-5, y=5