The nth Taylor polynomial for a function f at x0 is sometimes?

Question

referred to as the polynomial of degree at most n that best approximates f near x0.

a. explain why this description is accurate.

b. find the quadratic polynomial that best approximates a function f near x0=1 if the tangent line at x0=1 has equation y=4x-1 and if f"(1)=6.

Answer 1

So what is your problem? (a) and (b) are two completely independent questions. Have you tried to answer either of them?

The only element they have in common is the definition of a Taylor polynomial. If you don't know that, it is just a truncated Taylor series:

http://en.wikipedia.org/wiki/Taylor_seri...