Question 118651
Let N be the first number. 
Then N+10 is the second number.
Their product is N(N+10). 
{{{P=N(N+10)}}}
{{{P=N^2+10N}}}
To find a minimum, set the derivative of P with respect to N equal to zero. 
{{{dP/dN=2N+10}}}
Now set it equal to zero. 
{{{dP/dN=2N+10=0}}}
{{{2N=-10}}}
{{{N=-5}}}
{{{N+10=5}}}
Graphically, the product function N(N+10) shows the same result. 
Here x=N and y=N(N+10).
{{{ graph( 300, 300, -10, 10, -100, 100, x^2+10x) }}}
The first number is -5.
The second number is 5.
Their product is -25.