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Consider the following. (If an answer does not exist, enter DNE.) f'(x) = x2 + x - 30 (a) Find the open intervals on which f'(x) is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing

Consider the following. (If an answer does not exist, enter DNE.) f'(x) = x2 + x - 30 (a) Find the open intervals on which f'(x) is increasing or decreasing. (Enter your answers using interval notation.) increasing decreasing

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 Consider the following problem regarding the function \( f'(x) = x^2 + x - 30 \). ### (a) Increasing or Decreasing Intervals Find the open intervals on which \( f'(x) \) is increasing or decreasing. (Enter your answers using interval notation.) - **Increasing:** [ ] - **Decreasing:** [ ] ### (b) Concavity of the Graph Find the open intervals on which the graph of \( f \) is concave upward or concave downward. (Enter your answers using interval notation.) - **Concave Upward:** [ ] - **Concave Downward:** [ ] ### (c) Relative Extrema and Inflection Points Find the \( x \)-values of the relative extrema of \( f \). (Enter your answers as a comma-separated list.) - **Relative Maximum \( x = \):** [ ] - **Relative Minimum \( x = \):** [ ] Find the \( x \)-values of the inflection points of \( f \). (Enter your answers as a comma-separated list.) - \( x = \) [ ]
Transcribed Image Text:## Problem Statement Consider the following problem regarding the function \( f'(x) = x^2 + x - 30 \). ### (a) Increasing or Decreasing Intervals Find the open intervals on which \( f'(x) \) is increasing or decreasing. (Enter your answers using interval notation.) - **Increasing:** [ ] - **Decreasing:** [ ] ### (b) Concavity of the Graph Find the open intervals on which the graph of \( f \) is concave upward or concave downward. (Enter your answers using interval notation.) - **Concave Upward:** [ ] - **Concave Downward:** [ ] ### (c) Relative Extrema and Inflection Points Find the \( x \)-values of the relative extrema of \( f \). (Enter your answers as a comma-separated list.) - **Relative Maximum \( x = \):** [ ] - **Relative Minimum \( x = \):** [ ] Find the \( x \)-values of the inflection points of \( f \). (Enter your answers as a comma-separated list.) - \( x = \) [ ]
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