Find the 5th degree Taylor polynomial for the function f(x) = cos x at .
We take some derivatives and evaluate them at . Since , we don't even have to think to evaluate half of these derivatives.
Then we plug the values into the formula, making sure we keep parentheses in the right places and keep track of the negative signs:
Graphing f(x) and g(x), we see the functions f(x) and (C) from the previous exercise: