Answer:
Answer: {-5, 5}. Product is -25, which is the minimum.
Step-by-step explanation:
let a, b denote the two numbers. We know that b-a=10.
We are looking for a minimum over the product a*b.
One can minimize this using derivatives. In case you have not yet had derivatives, you can also use the vertex of a parabola (since the above is a quadratic form):
The minimum is at the vertex a=-5 and so b=5
Their distance is 10, and their product attains the minimum value of all possiblities -25.
Answer:
Step-by-step explanation:
let the numbers be x and y,let y>x
y-x=10
y=x+10
product P=xy=x(x+10)=x²+10x
[tex]\frac{dP}{dx} =2x+10\\\frac{dP}{dx} =0,gives\\2x+10=0\\2x=-10\\x=-5\\\frac{d^2P}{dx^2} =2>0 ~at~x=-5\\[/tex]
∴P is minimum at x=-5
y=x+10=-5+10=5
numbers are -5,5
