## monroe17 Group Title find two numbers a and b (with a≤b) whose difference is 38 and whose product is minimized one year ago one year ago

1. satellite73 Group Title

if one number is $$x$$ and the other is $$y$$ then their difference is $$x-y=38$$ making $$y=x-38$$

2. satellite73 Group Title

you want to minimize the product $x(x-38)=x^2-38x$

3. satellite73 Group Title

minimum will be at the vertex $$-\frac{b}{2a}=-\frac{-38}{2}=19$$

4. carson889 Group Title

Or it can be found by finding the critical point. That is, where the derivative of the above found product is equal to zero. So the derivative of $x ^{2} -38x$ is $2x - 38$, set it equal to zero and solve for x, x = 19.

5. monroe17 Group Title

got it! 19 and -19 (: thanks!