Consider the function f(x) = 2r + 3r² – 7. a) Find the intervals where the graph of f(r) is increasing, and where it is decreasing. b) Find any relative extrema.
Consider the function f(x) = 2r + 3r² – 7. a) Find the intervals where the graph of f(r) is increasing, and where it is decreasing. b) Find any relative extrema.
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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Transcribed Image Text:### Problem 2: Function Analysis
Consider the function \( f(x) = 2x^3 + 3x^2 - 7 \).
#### Tasks:
a) **Determine Intervals of Increase and Decrease:**
- Identify the intervals where the graph of \( f(x) \) is increasing.
- Identify the intervals where the graph of \( f(x) \) is decreasing.
b) **Find Relative Extrema:**
- Locate any relative extrema of the function \( f(x) \).
This problem involves analyzing the behavior of a cubic function to understand its increasing and decreasing nature as well as identifying any peaks or valleys (relative extrema) on the graph.
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