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7. What does the critical point(s) mean to the graph of the function? Determine the critical point(s) ( if exist) of (x) = x* – 2x° + x² – 1 [C: 3]

7. What does the critical point(s) mean to the graph of the function? Determine the critical point(s) ( if exist) of (x) = x* – 2x° + x² – 1 [C: 3]

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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**Question 7:** What does the critical point(s) mean to the graph of the function? Determine the critical point(s) (if they exist) of \( f(x) = x^4 - 2x^3 + x^2 - 1 \). **[C: 3]** --- **Explanation:** Critical points of a function occur where the derivative \( f'(x) \) is zero or undefined. These points are significant because they can indicate local maximums, local minimums, or points of inflection on the graph of the function. Understanding critical points helps in analyzing the behavior of the function. - To determine the critical points, find \( f'(x) \) and solve for when \( f'(x) = 0 \) or where it is undefined. - In this context, \( [C: 3] \) might indicate a specific critical point value or result to consider, possibly as a solution check.
Transcribed Image Text:**Question 7:** What does the critical point(s) mean to the graph of the function? Determine the critical point(s) (if they exist) of \( f(x) = x^4 - 2x^3 + x^2 - 1 \). **[C: 3]** --- **Explanation:** Critical points of a function occur where the derivative \( f'(x) \) is zero or undefined. These points are significant because they can indicate local maximums, local minimums, or points of inflection on the graph of the function. Understanding critical points helps in analyzing the behavior of the function. - To determine the critical points, find \( f'(x) \) and solve for when \( f'(x) = 0 \) or where it is undefined. - In this context, \( [C: 3] \) might indicate a specific critical point value or result to consider, possibly as a solution check.
Expert Solution
Step 1

Critical points of graph of function

points on graph of function where derivative is zero or derivative doesn't exist

Steps to find the critical points:

1.find the  first derivative of given function

2.set the derivative to zero to find the critical points

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