uestion 21 W f(x) f'(x) f"(x) f'(x) f(4)(x) 15 4 5 -1 23 1 8 3 -2 Let fbe a function having derivatives of all orders for all real numbers. Selected values of fand its first four derivatives are shown in the table above. Write the second-degree Taylor polynomial for fabout x = 0 and use it to approximate f(0.2). Let g be a function such that g(z) = f(x3). Write the fifth-degree Taylor polynomial for g', the derivative of g, about a = 0. Write the third-degree Tavlor polynomial for fabout z = 1.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 20E
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I only need parts B and D. And the question does not allow a calculator to be used. Thank you!

Question 21 A
f(x)
f'(x)
f"(x)
f"'(x)
f(4)(x)
4
5
-1
15
23
3
1
8
3
-2
6. Let fbe a function having derivatives of all orders for all real numbers. Selected values of fand its first four derivatives are shown in the table above.
(a) Write the second-degree Taylor polynomial for fabout x = 0 and use it to approximate f(0.2).
(b) Let g be a function such that g(z) = f(x3). Write the fifth-degree Taylor polynomial for g', the derivative of g, about x = 0.
(c) Write the third-degree Taylor polynomial for fabout a = 1.
(d) It is known that |f(4 (x) < 300 for 0 <a< 1.125. The third-degree Taylor polynomial for fabout = 1, found in part (c), is used to approximate f(1.1). Use the Lagrange error bound along with the information about f(4) (x) to find an upper bound on the error of the
approximation.
Transcribed Image Text:Question 21 A f(x) f'(x) f"(x) f"'(x) f(4)(x) 4 5 -1 15 23 3 1 8 3 -2 6. Let fbe a function having derivatives of all orders for all real numbers. Selected values of fand its first four derivatives are shown in the table above. (a) Write the second-degree Taylor polynomial for fabout x = 0 and use it to approximate f(0.2). (b) Let g be a function such that g(z) = f(x3). Write the fifth-degree Taylor polynomial for g', the derivative of g, about x = 0. (c) Write the third-degree Taylor polynomial for fabout a = 1. (d) It is known that |f(4 (x) < 300 for 0 <a< 1.125. The third-degree Taylor polynomial for fabout = 1, found in part (c), is used to approximate f(1.1). Use the Lagrange error bound along with the information about f(4) (x) to find an upper bound on the error of the approximation.
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