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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Can you help me answer these 2 questions based on this graph.

Transcribed Image Text:**Transcription for Educational Website:**
A function \( f(x) \) is defined everywhere. The derivative graph, \( f'(x) \), is given below. Please answer questions 3-5 given this graph.
**Graph Description:**
The graph is a plot of \( y = f'(x) \) on a coordinate plane. The x-axis is labeled from 0 to 10 and the y-axis from -2 to 2.
- The curve begins at the bottom left, approaching the point (0, -2).
- It rises steadily to a local peak near (2, 2).
- The curve slightly dips around (3, 1) before rising to another peak at (5, 2).
- After descending to cross the x-axis at (7, 0), it reaches a trough at (8, -2).
- Finally, it ascends sharply, exiting the graph at the upper right.
This graph can be used to analyze the rate of change and critical points of the function \( f(x) \).

Transcribed Image Text:The image contains a graph of a function \( f(x) \) and a multiple-choice question regarding where the function is decreasing.
**Graph Explanation:**
- The graph shows a curve plotted on a coordinate plane with the x-axis labeled at intervals of 2 units (0, 2, 4, 6).
- The curve appears to decrease from the left of the origin and then increase at x = 0.
- It seems to increase from somewhere around x = 1 to x = 3, decrease between x = 3 and x = 5, and increase again from x = 5 to x = 7.
- The curve decreases again after x = 7.
**Question:**
Where is the function \( f(x) \) decreasing?
**Options:**
(a) \( (-\infty, 0) \)
(b) \( (2, 3) \cup (5, 7) \)
(c) \( (-\infty, 2) \cup (3, 5) \cup (7, \infty) \)
(d) \( (-\infty, 1) \cup (6, 8) \)
(e) \( (-\infty, 0) \cup (2, 3) \cup (6, 8) \)
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