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Exercise 7

Avg difficulty 2.5

Suppose we know the following information about a function ff: f(0)=2,f′(0)=−3,f′′(0)=−1,f′′′(0)=0,f(4)(0)=−3\begin{gathered} f(0) = 2, f'(0) = -3, f''(0) = -1, f'''(0) = 0, f^{(4)}(0) = -3 \end{gathered}.

  1. Determine T4(x)T_4(x), the degree 44 Taylor polynomial of ff that is centered at a=0a = 0.

  2. Use T4(x)T_4(x) to estimate f(0.5)f(0.5).

  3. State each of the Taylor polynomials T3(x)T_3(x), T2(x)T_2(x), and T1(x)T_1(x).

Boelkins, Active Calculus, §8.2 Taylor polynomials, Exercise 7

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Adapted from Active Calculus © 2012–2025 Matthew Boelkins. Licensed under CC BY-SA 4.0. Source: Active Calculus. Imported at revision dc86ba3.