Let f $($x$)=$ cos x$.$ Use Eq$.(4\mathrm{.}9)$ and the values of f $($x$)$ at x $=0\mathrm{.}25,0\mathrm{.}5,$ and $0\mathrm{.}75$ to approximate

f$(0\mathrm{.}5).$ Compare this result to the exact value and to the approximation found in Exercise $15$ of

Section $3\mathrm{.}5.$ Explain why this method is particularly accurate for this problem and find a bound for

the error.