Find the lowest degree polynomial that satisfies the following constraints:
iii)The maximum of F $F$ on the interval (0,1) $(0,1)$ occurs at point c $c$
iv) F(x) $F(x)$ is positive on the interval (0,1) $(0,1)$
The answer seems to depend pretty strongly on c. $c$. It's not difficult to find solutions for all c, $c$, but the solutions are not minimal. It seems like the solution involves Chebyshev polynomials, but I'm not familiar with them. Can anyone recommended a link?