Question 2 Consider the function f(x)=2x" ln(x + 8x+8). The function f is complicated enough that it is hard to find statinoray point (s) using direct calcula- tion. Assume that the function f has a stationary point at some point z = ze that is close to z = -1. Our goal is to find an approximate value of ro using Taylor polynomial of f(r) around r= -1. (a) Calculate the first and second derivatives f'(x) and f"(z) (no need to simplify the expressions). (b) Calculate the second-order Taylor polynomials (T₂f)(x) centred around z= -1. Show all working. (c) Determine the stationary point of the Taylor polynomial found in (b) (rounded to 2 decimal places as necessary) and determine its nature.
Question 2 Consider the function f(x)=2x" ln(x + 8x+8). The function f is complicated enough that it is hard to find statinoray point (s) using direct calcula- tion. Assume that the function f has a stationary point at some point z = ze that is close to z = -1. Our goal is to find an approximate value of ro using Taylor polynomial of f(r) around r= -1. (a) Calculate the first and second derivatives f'(x) and f"(z) (no need to simplify the expressions). (b) Calculate the second-order Taylor polynomials (T₂f)(x) centred around z= -1. Show all working. (c) Determine the stationary point of the Taylor polynomial found in (b) (rounded to 2 decimal places as necessary) and determine its nature.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Question 2 Consider the function
f(x)=2r" ln(2 +8x+8).
The function f is complicated enough that it is hard to find statinoray point (s) using direct calcula-
tion. Assume that the function f has a stationary point at some point z = zo that is close to z = -1.
Our goal is to find an approximate value of ro using Taylor polynomial of f(r) around 2 = −1.
(a) Calculate the first and second derivatives f'(r) and f"(z) (no need to simplify the expressions).
(b) Calculate the second-order Taylor polynomials (T₂f)(z) centred around 2 = -1. Show all
working.
(c) Determine the stationary point of the Taylor polynomial found in (b) (rounded to 2 decimal
places as necessary) and determine its nature.
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