Consider the following. f(x) = 4x x+5 Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. y 2- 07 -1- -2 0.5 O 3¹¹f'(x) 3 1 15 X f(x) y Of approaches ∞ when f' is zero. Of approaches -√2 when f' is zero. O f' is never zero. 2- 0 -1 Describe the behavior of the function when the derivative is zero. O f approaches √2 when f' is zero. --2 1 2 f(x) 3 f'(x) 2- f(x) f'(x) K f 0 0 1 2 3 4 5 0.5 1 1.5 2 3 4 5 f'(x) f(x) 2.5 3
Consider the following. f(x) = 4x x+5 Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes. y 2- 07 -1- -2 0.5 O 3¹¹f'(x) 3 1 15 X f(x) y Of approaches ∞ when f' is zero. Of approaches -√2 when f' is zero. O f' is never zero. 2- 0 -1 Describe the behavior of the function when the derivative is zero. O f approaches √2 when f' is zero. --2 1 2 f(x) 3 f'(x) 2- f(x) f'(x) K f 0 0 1 2 3 4 5 0.5 1 1.5 2 3 4 5 f'(x) f(x) 2.5 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![### Consider the following function:
\[ f(x) = \frac{4x}{\sqrt{x+5}} \]
Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes.
#### Graph Descriptions:
1. **Top Left Graph:**
- **Axes**: \( x \) from -1 to 3, \( y \) from -3 to 3.
- **Curves**:
- The function \( f(x) \) is graphed as a curve, showing variation along the \( x \)-axis.
- The derivative \( f'(x) \) is also plotted, showing zero crossings near \( x = 0.5 \).
2. **Top Right Graph:**
- **Axes**: \( x \) from 0 to 6, \( y \) from -3 to 3.
- **Curves**:
- Function \( f(x) \) and its derivative \( f'(x) \) are shown, illustrating changes in slope after \( x = 3 \).
3. **Bottom Left Graph:**
- **Axes**: \( x \) from 1 to 6, \( y \) from -3 to 3.
- **Curves**:
- Both \( f(x) \) and \( f'(x) \) are plotted, indicating behavior as \( x \) increases beyond 4.
4. **Bottom Right Graph:**
- **Axes**: \( x \) from 0 to 3, \( y \) from -3 to 3.
- **Curves**:
- Function \( f(x) \), along with \( f'(x) \), shows a more detailed view of the initial changes and behavior near \( x = 1 \).
### Describe the behavior of the function when the derivative is zero.
- \( f \) approaches \(\sqrt{2}\) when \( f' \) is zero.
- \( f \) approaches \(\infty\) when \( f' \) is zero.
- \( f \) approaches \(-\sqrt{2}\) when \( f' \) is zero.
- \( f' \) is never zero.
\[ \circ \] \( f \) approaches \(\sqrt{2}\) when \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6b3477-66d3-4452-8b0f-11f5e6ce06e0%2Feeee79e3-1c34-412d-b7e9-0c3e500f1f96%2Fsx7s84a_processed.png&w=3840&q=75)
Transcribed Image Text:### Consider the following function:
\[ f(x) = \frac{4x}{\sqrt{x+5}} \]
Use a computer algebra system to find the derivative of the function. Then use the utility to graph the function and its derivative on the same set of coordinate axes.
#### Graph Descriptions:
1. **Top Left Graph:**
- **Axes**: \( x \) from -1 to 3, \( y \) from -3 to 3.
- **Curves**:
- The function \( f(x) \) is graphed as a curve, showing variation along the \( x \)-axis.
- The derivative \( f'(x) \) is also plotted, showing zero crossings near \( x = 0.5 \).
2. **Top Right Graph:**
- **Axes**: \( x \) from 0 to 6, \( y \) from -3 to 3.
- **Curves**:
- Function \( f(x) \) and its derivative \( f'(x) \) are shown, illustrating changes in slope after \( x = 3 \).
3. **Bottom Left Graph:**
- **Axes**: \( x \) from 1 to 6, \( y \) from -3 to 3.
- **Curves**:
- Both \( f(x) \) and \( f'(x) \) are plotted, indicating behavior as \( x \) increases beyond 4.
4. **Bottom Right Graph:**
- **Axes**: \( x \) from 0 to 3, \( y \) from -3 to 3.
- **Curves**:
- Function \( f(x) \), along with \( f'(x) \), shows a more detailed view of the initial changes and behavior near \( x = 1 \).
### Describe the behavior of the function when the derivative is zero.
- \( f \) approaches \(\sqrt{2}\) when \( f' \) is zero.
- \( f \) approaches \(\infty\) when \( f' \) is zero.
- \( f \) approaches \(-\sqrt{2}\) when \( f' \) is zero.
- \( f' \) is never zero.
\[ \circ \] \( f \) approaches \(\sqrt{2}\) when \(
Expert Solution
Step 1: We write what we have to find out and given
We have a function. Then we have to find derivative of that function and draw the graph.
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
