Let f be a function that has derivatives of all orders for all real numbers. Assume that f(3)=1, f'(3)=4, f"(3)=6, and f'''(3)=12.
a) Write the third order Taylor polynomial for f at x=3 and use it to approximate f(3.2).
b) Does the linearization of f underestimate or overestimate the values of f(x) near x=3? Justify your answer.
For part a), I know how to find the third order Taylor polynomial but I don't know how to approximate f(3.2), please show all your work for that. And for part c), please show all your work as well. Thanks.