Can you answer this Calculus question?

Question

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. 

Answer 1

a) Just substitute 3.2 for x in your Taylor polynomial approximation.

 

You didn't give a part c.