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Problem 2. Set p(x) = x³ + ax² + bx + c. (a) Show that the graph of p has exactly one point of inflection. What is x at that (b) Show that p has two local extreme values iff a? > 36. (c) diction.) Show that p cannot have only one local extreme value. (Hint: prove by contra-

Problem 2. Set p(x) = x³ + ax² + bx + c. (a) Show that the graph of p has exactly one point of inflection. What is x at that (b) Show that p has two local extreme values iff a? > 36. (c) diction.) Show that p cannot have only one local extreme value. (Hint: prove by contra-

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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**Problem 2:** Set \( p(x) = x^3 + ax^2 + bx + c \). (a) Show that the graph of \( p \) has exactly one point of inflection. What is \( x \) at that point? (b) Show that \( p \) has two local extreme values if and only if \( a^2 > 3b \). (c) Show that \( p \) cannot have only one local extreme value. (Hint: prove by contradiction.)
Transcribed Image Text:**Problem 2:** Set \( p(x) = x^3 + ax^2 + bx + c \). (a) Show that the graph of \( p \) has exactly one point of inflection. What is \( x \) at that point? (b) Show that \( p \) has two local extreme values if and only if \( a^2 > 3b \). (c) Show that \( p \) cannot have only one local extreme value. (Hint: prove by contradiction.)
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