Find two numbers with a difference of 10 and a product that is a minimum. find the minimum.

{-5, 5}. Product is -25, which is the minimum.

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.

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6

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