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If ?(?) = ?4 – 12?2 + 7, how many critical points and inflection points are there? Select one: a. 2 critical points and 0 inflection points O b. 2 critical points and 1 inflection point O c. 3 critical points and 2 inflection points O d. 2 critical points and 1 inflection point e. 2 critical points and 2 inflection points O O

If ?(?) = ?4 – 12?2 + 7, how many critical points and inflection points are there? Select one: a. 2 critical points and 0 inflection points O b. 2 critical points and 1 inflection point O c. 3 critical points and 2 inflection points O d. 2 critical points and 1 inflection point e. 2 critical points and 2 inflection points O O

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 Statement If \( f(x) = x^4 - 12x^2 + 7 \), how many critical points and inflection points are there? ### Options Select one: - **a.** 2 critical points and 0 inflection points - **b.** 2 critical points and 1 inflection point - **c.** 3 critical points and 2 inflection points - **d.** 2 critical points and 1 inflection point - **e.** 2 critical points and 2 inflection points ### Explanation The goal is to find the number of critical points and inflection points for the function \( f(x) = x^4 - 12x^2 + 7 \). 1. **Critical Points:** These occur where the first derivative \( f'(x) \) is equal to zero or is undefined. 2. **Inflection Points:** These occur where the second derivative \( f''(x) \) changes sign. This exercise involves calculating derivatives, setting them to zero, and solving for \( x \) to determine the points of interest.
Transcribed Image Text:### Problem Statement If \( f(x) = x^4 - 12x^2 + 7 \), how many critical points and inflection points are there? ### Options Select one: - **a.** 2 critical points and 0 inflection points - **b.** 2 critical points and 1 inflection point - **c.** 3 critical points and 2 inflection points - **d.** 2 critical points and 1 inflection point - **e.** 2 critical points and 2 inflection points ### Explanation The goal is to find the number of critical points and inflection points for the function \( f(x) = x^4 - 12x^2 + 7 \). 1. **Critical Points:** These occur where the first derivative \( f'(x) \) is equal to zero or is undefined. 2. **Inflection Points:** These occur where the second derivative \( f''(x) \) changes sign. This exercise involves calculating derivatives, setting them to zero, and solving for \( x \) to determine the points of interest.
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