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Let f(x) = x ln(x²) - : Use the second derivative test to find the local min/max of f(x). f''(x) = At this point, you should find the critical points of f and test the sign of f'' there. f has a local max of f has a local min of at x = at x = Further, the graph changes concavity at x =

Let f(x) = x ln(x²) - : Use the second derivative test to find the local min/max of f(x). f''(x) = At this point, you should find the critical points of f and test the sign of f'' there. f has a local max of f has a local min of at x = at x = Further, the graph changes concavity at x =

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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Let \( f(x) = x \ln(x^2) - x \). Use the second derivative test to find the local min/max of \( f(x) \). \[ f''(x) = \quad \text{\_\_\_\_\_\_\_\_\_\_\_} \] At this point, you should find the critical points of \( f \) and test the sign of \( f'' \) there. - \( f \) has a local max of \[ \quad \text{\_\_\_\_\_\_\_} \quad \] at \( x = \quad \text{\_\_\_\_\_\_\_} \) - \( f \) has a local min of \[ \quad \text{\_\_\_\_\_\_\_} \quad \] at \( x = \quad \text{\_\_\_\_\_\_\_} \) Further, the graph changes concavity at \( x = \quad \text{\_\_\_\_\_\_\_} \) from concave \(\quad \text{[Select an answer]} \quad\) to concave \(\quad \text{[Select an answer]} \quad\). Now try to sketch a graph of \( f(x) \) on your own paper, noting the min, max, and inflection point(s). (Don't worry about the \( x \)-intercepts.) After entering your answers, click "Show Answer" or "Jump to Answer" to check your graph.
Transcribed Image Text:Let \( f(x) = x \ln(x^2) - x \). Use the second derivative test to find the local min/max of \( f(x) \). \[ f''(x) = \quad \text{\_\_\_\_\_\_\_\_\_\_\_} \] At this point, you should find the critical points of \( f \) and test the sign of \( f'' \) there. - \( f \) has a local max of \[ \quad \text{\_\_\_\_\_\_\_} \quad \] at \( x = \quad \text{\_\_\_\_\_\_\_} \) - \( f \) has a local min of \[ \quad \text{\_\_\_\_\_\_\_} \quad \] at \( x = \quad \text{\_\_\_\_\_\_\_} \) Further, the graph changes concavity at \( x = \quad \text{\_\_\_\_\_\_\_} \) from concave \(\quad \text{[Select an answer]} \quad\) to concave \(\quad \text{[Select an answer]} \quad\). Now try to sketch a graph of \( f(x) \) on your own paper, noting the min, max, and inflection point(s). (Don't worry about the \( x \)-intercepts.) After entering your answers, click "Show Answer" or "Jump to Answer" to check your graph.
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