Chapter 6.3, Problem 138E

In the following exercises, the maximum of the right-hand side of the remainder estimate on $\left|R_1\right|\le \frac{\max |f"(z)|}{2}{R}^2$ on [a-R, a+R] occurs at a or a ± R. Estimate the maximum value of R such that $\frac{\max |f"(z)|}{2}{R}^2\le 0.1$ on [a - R, a + R] by plotting this maximum as a function of R.

138. [T] in x approximated by x - 1, a = 1