I have been asked to do the following:

Suppose that f is a function with the property that |$\displaystyle f^n(x)$|$\displaystyle \leq$3 for all n and for all x on [-1,1].

a. Estimate the error if the Taylor polynomial $\displaystyle p_{n}$(x) (in powers of x) with n=4 is used to approximate f($\displaystyle \frac{1}{2}$).

b. Find the least positive integer n such that $\displaystyle p_{n}$(x) (in powers of x) will approximate f on [-1,1] to within .001.

I don't know where to start on this problem. I have no f(x) to work with so what do I do?