Hello i got this problem and i have no idea what to do:

Among polynomials of third degree with coefficients in find such for which is value minimal.

Thanks for any help

Printable View

- May 19th 2011, 04:48 AMtoken22Polynomial
Hello i got this problem and i have no idea what to do:

Among polynomials of third degree with coefficients in find such for which is value minimal.

Thanks for any help - May 19th 2011, 08:36 AMOpalg
You need some additional condition for this problem to make much sense. As it stands, the max value of the polynomial could be arbitrarily low. For example, if then the max value on the interval [–1,1] is .

My first thought was that the quantity to be minimised should be |f(x)|. But that is no better, because for example the function has max absolute value as close as you like to 0, for sufficiently small .