Example 3-3-2 - Maple Help



Chapter 3: Applications of Differentiation



Section 3.3: Taylor Polynomials



Example 3.3.2



 a) With $f$ and ${P}_{3}$ as in Example 3.3.1, obtain ${R}_{3}\left(x\right)$ and use it to estimate the largest difference between $f$ and ${P}_{3}$ on $\left[-1,1\right]$. Hence, obtain the maximum value of $\left|{R}_{4}\right|$ = $\left|\frac{{f}^{\left(4\right)}\left(c\right)}{4!}{x}^{4}\right|$, which in turn requires finding the maximal value of $\left|{f}^{\left(4\right)}\left(c\right)\right|$ for $-1\le c\le 1$.
 b) Find the actual value of the largest difference between $f$ and ${P}_{3}$ on $\left[-1,1\right]$.







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