Given an arbitrary continuous function f(x), let Pn(x) be the polynomial of degree at most n that approximates f(x) in the least squares sense. Is it true that Pn(x) interpolates f(x) at n + 1 points? Prove it if it is true or disprove it by giving a counterexample.
Hi, this is a past paper problem I am trying to solve. I can do so for a normal polynomial interpolation, but the least squares thing is confusing me