Given the graph of the function y= f(z), list the following lettered values (A to D) in order from smallest to largest. %3D 14 13 12 11 10 -1 A: the average rate of change of fover the interval [2, 4] B: the instantaneous rate of change of f at a = 1.5 C: f'(3) D: f'(2.5)
Given the graph of the function y= f(z), list the following lettered values (A to D) in order from smallest to largest. %3D 14 13 12 11 10 -1 A: the average rate of change of fover the interval [2, 4] B: the instantaneous rate of change of f at a = 1.5 C: f'(3) D: f'(2.5)
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:**
Given the graph of the function \( y = f(x) \), list the following lettered values (A to D) in order from smallest to largest.
**Graph Description:**
The graph is a smooth, continuous curve that shows the behavior of the function \( y = f(x) \). The x-axis ranges from 0 to 5, and the y-axis ranges from -2 to 14. The key points on the curve include several peaks and troughs, indicating changes in the slope of the function.
---
**Lettered Values:**
- **A:** The average rate of change of \( f \) over the interval \([2, 4]\).
- **B:** The instantaneous rate of change of \( f \) at \( x = 1.5 \).
- **C:** \( f'(3) \).
- **D:** \( f'(2.5) \).
---
**Instructions:**
Determine the values of A, B, C, and D based on the graph and rank them from smallest to largest.
When analyzing each lettered value:
- **A:** Calculate the slope between \( x = 2 \) and \( x = 4 \).
- **B, C, D:** Estimate the derivative \( f'(x) \) at the specified points by evaluating the slope of the tangent line at those x-values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F868b8534-4d89-4d63-908b-b662dc9aeef4%2Ff7782ad3-7486-491b-8d0f-e92e64bfb719%2Fitcbp7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given the graph of the function \( y = f(x) \), list the following lettered values (A to D) in order from smallest to largest.
**Graph Description:**
The graph is a smooth, continuous curve that shows the behavior of the function \( y = f(x) \). The x-axis ranges from 0 to 5, and the y-axis ranges from -2 to 14. The key points on the curve include several peaks and troughs, indicating changes in the slope of the function.
---
**Lettered Values:**
- **A:** The average rate of change of \( f \) over the interval \([2, 4]\).
- **B:** The instantaneous rate of change of \( f \) at \( x = 1.5 \).
- **C:** \( f'(3) \).
- **D:** \( f'(2.5) \).
---
**Instructions:**
Determine the values of A, B, C, and D based on the graph and rank them from smallest to largest.
When analyzing each lettered value:
- **A:** Calculate the slope between \( x = 2 \) and \( x = 4 \).
- **B, C, D:** Estimate the derivative \( f'(x) \) at the specified points by evaluating the slope of the tangent line at those x-values.
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