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A critical value such that f"(x)=0is called a stationary point. a) Show that both of the functions f(x)=(x-1)" and g(x)=x'-3x² + 3x- 2 have stationary points at x=1. b) What does the first derivative test tell you about the nature of these stationary points? (max/min} c) What does the second derivative test tell you about the nature of these stationary points? (concavity)

A critical value such that f"(x)=0is called a stationary point. a) Show that both of the functions f(x)=(x-1)" and g(x)=x'-3x² + 3x- 2 have stationary points at x=1. b) What does the first derivative test tell you about the nature of these stationary points? (max/min} c) What does the second derivative test tell you about the nature of these stationary points? (concavity)

Calculus: Early Transcendentals
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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Can you please help me solve this. Specifically questions b and c

A critical value such that f"(x)= 0is called a stationary point. a) Show that both of the functions f(x)=(x-1)' and g(x)=x' – 3x² + 3x –2 have stationary points at x=1. b) What does the first derivative test tell you about the nature of these stationary points? (max/min} c) What does the second derivative test tell you about the nature of these stationary points? (concavity)
Transcribed Image Text:A critical value such that f"(x)= 0is called a stationary point. a) Show that both of the functions f(x)=(x-1)' and g(x)=x' – 3x² + 3x –2 have stationary points at x=1. b) What does the first derivative test tell you about the nature of these stationary points? (max/min} c) What does the second derivative test tell you about the nature of these stationary points? (concavity)
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