Draw the graph of a function f such that f(1) = f'(1) = f"(1) = 1. Draw the linear approximation to the function at the point (1, 1). Now draw the graph of another function g such that g(1) = g'(1) = 1 and g"(1) = 10. (It is not possible to represent the second derivative exactly, but your graphs should reflect the fact that f"(1) is relatively small and g"(1) is relatively large.) Now suppose that linear approximations are used to approximate f(1.1) and g(1.1). 

a. Which function value has the more accurate linear approximation near x = 1 and why?

b. Explain why the error in the linear approximation to f near a point a is proportional to the magnitude of f"(a).