The graph of a function y = f (x) is shown below. Which of the following statements are true? I. f'(-1) does not exist. II. f'(1) = 1 III. f'(2) does not exist because of a sharp corner. IV. f'(2) does not exist because f (x) is not continuous at x = 2. V. f'(3) < 0 VI. f'(3) > 0 a) O I, II, IV and V only b) O III and VI only c) OI, III, IV and V only d) OI, II, III, IV, V and VI e) II, III, IV and VI only

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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**Graph Analysis of a Function \( y = f(x) \)**

The image presents a graph of a function \( y = f(x) \).

### Graph Description
The graph shows the curve of function \( f(x) \) over a certain range. It includes important critical points and features such as sharp corners and areas of continuity or discontinuity. The x-axis and y-axis are labeled with integer values.

### Statements Analysis
The task is to evaluate which of the following statements about the function and its derivative are true:

I. \( f'(-1) \) does not exist.
II. \( f'(1) = 1 \)
III. \( f'(2) \) does not exist because of a sharp corner.
IV. \( f'(2) \) does not exist because \( f(x) \) is not continuous at \( x = 2 \).
V. \( f'(3) < 0 \)
VI. \( f'(3) > 0 \)

### Options
a) I, II, IV, and V only  
b) III and VI only  
c) I, III, IV, and V only  
d) I, II, III, IV, V, and VI  
e) II, III, IV, and VI only  

Analysis requires understanding of derivative behavior at sharp corners, points of continuity, and the slope of the function at given points.
Transcribed Image Text:**Graph Analysis of a Function \( y = f(x) \)** The image presents a graph of a function \( y = f(x) \). ### Graph Description The graph shows the curve of function \( f(x) \) over a certain range. It includes important critical points and features such as sharp corners and areas of continuity or discontinuity. The x-axis and y-axis are labeled with integer values. ### Statements Analysis The task is to evaluate which of the following statements about the function and its derivative are true: I. \( f'(-1) \) does not exist. II. \( f'(1) = 1 \) III. \( f'(2) \) does not exist because of a sharp corner. IV. \( f'(2) \) does not exist because \( f(x) \) is not continuous at \( x = 2 \). V. \( f'(3) < 0 \) VI. \( f'(3) > 0 \) ### Options a) I, II, IV, and V only b) III and VI only c) I, III, IV, and V only d) I, II, III, IV, V, and VI e) II, III, IV, and VI only Analysis requires understanding of derivative behavior at sharp corners, points of continuity, and the slope of the function at given points.
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