If 1000 people are sitting around a circular table and each person makes a donation of the average of the two people sitting adjacent to him/her and it is known that one person made a contribution of 500 dollars, then find, if you can, the total amount donated and the maximum amount of money donated.
If is a polynomial such that and all the 11 coefficients are positive, then answer true or false for the following questions:
p(x) has a global minimum.
are all positive.
p'(x) has all negative real roots.