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13. For f(x) = -x³ + 3x² + 9x, find the followings. a) Find f'(x) and the critical points. b) Determine the intervals on which fis increasing or decreasing. Then find the local maximum and minimum values of f. Use the first derivative test." Intervals Test point Sign of f'(x) Conclusion (Inc Dec) Local Maximum Maxima: Local Minimum Minima:

13. For f(x) = -x³ + 3x² + 9x, find the followings. a) Find f'(x) and the critical points. b) Determine the intervals on which fis increasing or decreasing. Then find the local maximum and minimum values of f. Use the first derivative test." Intervals Test point Sign of f'(x) Conclusion (Inc Dec) Local Maximum Maxima: Local Minimum Minima:

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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13. For f(x) = x³ + 3x2 + 9x, find the followings. Find f'(x) and the critical points. a) b) Determine the intervals on which f is increasing or decreasing. Then find the local maximum and minimum values of f. Use the first derivative test. Intervals Test point Sign of f'(x) Conclusion (Inc/Dec) Local Maximum/Maxima: Local Minimum/Minima:
Transcribed Image Text:13. For f(x) = x³ + 3x2 + 9x, find the followings. Find f'(x) and the critical points. a) b) Determine the intervals on which f is increasing or decreasing. Then find the local maximum and minimum values of f. Use the first derivative test. Intervals Test point Sign of f'(x) Conclusion (Inc/Dec) Local Maximum/Maxima: Local Minimum/Minima:
c) Find the intervals of concavity and the inflection points. f"(x)= Intervals Test point Sign of f" (x) Conclusion (CU/CD) Inflection point(s):
Transcribed Image Text:c) Find the intervals of concavity and the inflection points. f"(x)= Intervals Test point Sign of f" (x) Conclusion (CU/CD) Inflection point(s):
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