Chapter 9.7, Problem 15E

Conjecture Consider the function $f(x)=\cos x$ and its Maclaurin polynomials $P_2$, $P_4$, and $P_6$ (see Example 5).

(a) Use a graphing utility to graph f and the indicated polynomial approximations.

(b) Evaluate and compare the values of $f^n(0)$ and $P_n^{(n)}(0)$ for $n=2,4,$, and 6.

(c) Use the results in part (b) to make a conjecture about $f^n(0)$ and $P_n^{(n)}(0)$.