## anonymous 3 years ago find two numbers a and b (with a≤b) whose difference is 38 and whose product is minimized

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. carson889

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. anonymous

got it! 19 and -19 (: thanks!