Attempt
We can think of this as interpolating $(x_i, f(x_i))$ where $i=0,1,2$. Let $p(x)$ be the the polynomial we want. We can start by
$$ p(x) = f(x) + (x-x_0)A $$
taking derivative we obtain $p'(x) = f'(x) + A $ So, we can write now
$$ p(x) = f(x) + (x-x_0) (f'(x)-p'(x)) $$
Now notice that $p(x_1) = f(x_1)$ as desired. All we need now is to interpolate $x_2$. How can we do this? Is my approach correct so far ?