Use the given graph of f(x) to find the intervals on which f'(x) > 0. O A. f'(x) > 0 on [-6,6], f'(x) < 0 on (- o, - 6] U [6,00) O B. f'(x) > 0 on [- 36,36], f'(x) < 0 on (– o, – 36] U [36,00) c. f(x) > 0 on (- 0,6], f'(x) < 0 on [6,00) O D. f'(x) > 0 on (- o, - 6] U [6,0), f'(x) < 0 on [-6,6] 500- 400- 300- 200- 100- -12-10-8 -6 -4 -2 -100 2 4 6 8 1d 12 -200- 300- -400- -500-
Use the given graph of f(x) to find the intervals on which f'(x) > 0. O A. f'(x) > 0 on [-6,6], f'(x) < 0 on (- o, - 6] U [6,00) O B. f'(x) > 0 on [- 36,36], f'(x) < 0 on (– o, – 36] U [36,00) c. f(x) > 0 on (- 0,6], f'(x) < 0 on [6,00) O D. f'(x) > 0 on (- o, - 6] U [6,0), f'(x) < 0 on [-6,6] 500- 400- 300- 200- 100- -12-10-8 -6 -4 -2 -100 2 4 6 8 1d 12 -200- 300- -400- -500-
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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![**Instruction: Finding Intervals of Positive Derivative from Graph**
Below is a graph of the function \( f(x) \). Your task is to determine the intervals where the derivative \( f'(x) \) is greater than zero, which indicates where the function is increasing.
**Graph Description:**
- The graph shows a cubic function plotted on a coordinate plane, stretching from \( x = -12 \) to \( x = 12 \).
- The \( x \)-axis ranges from \(-12\) to \(12\).
- The \( y \)-axis ranges from \(-500\) to \(500\).
- The curve dips to a minimum below the \( x \)-axis and rises to a maximum above the \( x \)-axis.
**Choices for the Intervals:**
- **A.** \( f'(x) > 0 \) on \([-6, 6]\), \(f'(x) < 0\) on \((-\infty, -6) \cup [6, \infty)\)
- **B.** \( f'(x) > 0 \) on \([-36, 36]\), \(f'(x) < 0\) on \((-\infty, -36) \cup [36, \infty)\)
- **C.** \( f'(x) > 0 \) on \((-\infty, 6]\), \(f'(x) < 0\) on \([6, \infty)\)
- **D.** \( f'(x) > 0 \) on \((-\infty, -6) \cup [6, \infty)\), \(f'(x) < 0\) on \([-6, 6)\)
**Solution Approach:**
- Examine the graph and identify where the slope of the tangent to the graph is positive (the function is increasing).
- Determine the correct interval(s) from the choices given above.
Use this information to evaluate and select the correct option.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f96280e-7946-4657-be35-195de970c83c%2F6048fa90-ea79-4152-910b-85bca76cf3f2%2Fimoq3y_processed.png&w=3840&q=75)
Transcribed Image Text:**Instruction: Finding Intervals of Positive Derivative from Graph**
Below is a graph of the function \( f(x) \). Your task is to determine the intervals where the derivative \( f'(x) \) is greater than zero, which indicates where the function is increasing.
**Graph Description:**
- The graph shows a cubic function plotted on a coordinate plane, stretching from \( x = -12 \) to \( x = 12 \).
- The \( x \)-axis ranges from \(-12\) to \(12\).
- The \( y \)-axis ranges from \(-500\) to \(500\).
- The curve dips to a minimum below the \( x \)-axis and rises to a maximum above the \( x \)-axis.
**Choices for the Intervals:**
- **A.** \( f'(x) > 0 \) on \([-6, 6]\), \(f'(x) < 0\) on \((-\infty, -6) \cup [6, \infty)\)
- **B.** \( f'(x) > 0 \) on \([-36, 36]\), \(f'(x) < 0\) on \((-\infty, -36) \cup [36, \infty)\)
- **C.** \( f'(x) > 0 \) on \((-\infty, 6]\), \(f'(x) < 0\) on \([6, \infty)\)
- **D.** \( f'(x) > 0 \) on \((-\infty, -6) \cup [6, \infty)\), \(f'(x) < 0\) on \([-6, 6)\)
**Solution Approach:**
- Examine the graph and identify where the slope of the tangent to the graph is positive (the function is increasing).
- Determine the correct interval(s) from the choices given above.
Use this information to evaluate and select the correct option.
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