Interpolation of three positive values at 0, 1 and 2 by a polynomial with non-negative coefficients

Question

I am asking myself the question: Let $ y_0, y_1, y_2 $ be positive real numbers. Is there always a polynomial $ f $ with non-negative real numbers as coefficients which satisfies $ f( i ) = y_i $ for $ i = 0, 1, 2 $?

Thanks for thinking about it.

Answer 1

Hint:
Suppose $y_0>y_1$. What do you get when you evaluate $f(1)-f(0)$ ?