Find quadratic polynomial which best fits the function f(x)=e^x and x=0, in the sense that g(0)= f(0), and g'(0) = f'(0), and g"(0) = f"(0).

g(x)=?

Let . Then



Meanwhile, since , you have .

It follows that , , and , so that the quadratic fit for that satisfies the given points is



Note that this is just the second-order Taylor polynomial for about .

The answer would be: b