Use the given graph to estimate the value of each derivative. (Round all answers to one decimal place.) y = f(x) 1 (a) f'(-3) 1 2 (b) f'(-2) 2 1 (c) f'(-1) 3 0 (d) f'(0) 4 -2 (e) f' (1) 5 0 (f) f'(2) 6 1 (g) f'(3) 72 0 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question

Just need help with part (d). I don't understand why the answer isn't -2.

### Estimating Derivative Values from a Graph

To estimate the value of each derivative using the given graph of \( y = f(x) \), follow the instructions and use the visual representation to deduce the slopes at various points. Round all answers to one decimal place.

#### Graph Description:
The provided graph represents a function \( y = f(x) \) plotted on a Cartesian plane. The x-axis ranges from \(-4\) to \(4\) and the y-axis ranges from \(-1\) to \(1\). 

#### Exercise:
Estimate the value of each derivative at specified points:

1. **\( f' (-3) \):**
   - **Correct Answer:** 1.2
2. **\( f' (-2) \):**
   - **Correct Answer:** 2.1
3. **\( f' (-1) \):**
   - **Correct Answer:** 0.0
4. **\( f' (0) \):**
   - **Correct Answer:** -2.5
5. **\( f' (1) \):**
   - **Correct Answer:** 0.0
6. **\( f' (2) \):**
   - **Correct Answer:** 1.6
7. **\( f' (3) \):**
   - **Correct Answer:** 2.7

### Detailed Explanations:
- For each point listed (e.g., \(-3, -2, \ldots, 3\)), analyze the slope of the tangent line to the curve \( y = f(x) \).
- The slope at a point can be visually estimated by observing whether the curve is increasing or decreasing and how steep the incline or decline is.
- Use a consistent method to estimate each slope to one decimal place.

By following these steps, you ensure that you can estimate the slopes (derivatives) as accurately as possible using the visual graph provided.
Transcribed Image Text:### Estimating Derivative Values from a Graph To estimate the value of each derivative using the given graph of \( y = f(x) \), follow the instructions and use the visual representation to deduce the slopes at various points. Round all answers to one decimal place. #### Graph Description: The provided graph represents a function \( y = f(x) \) plotted on a Cartesian plane. The x-axis ranges from \(-4\) to \(4\) and the y-axis ranges from \(-1\) to \(1\). #### Exercise: Estimate the value of each derivative at specified points: 1. **\( f' (-3) \):** - **Correct Answer:** 1.2 2. **\( f' (-2) \):** - **Correct Answer:** 2.1 3. **\( f' (-1) \):** - **Correct Answer:** 0.0 4. **\( f' (0) \):** - **Correct Answer:** -2.5 5. **\( f' (1) \):** - **Correct Answer:** 0.0 6. **\( f' (2) \):** - **Correct Answer:** 1.6 7. **\( f' (3) \):** - **Correct Answer:** 2.7 ### Detailed Explanations: - For each point listed (e.g., \(-3, -2, \ldots, 3\)), analyze the slope of the tangent line to the curve \( y = f(x) \). - The slope at a point can be visually estimated by observing whether the curve is increasing or decreasing and how steep the incline or decline is. - Use a consistent method to estimate each slope to one decimal place. By following these steps, you ensure that you can estimate the slopes (derivatives) as accurately as possible using the visual graph provided.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,