Consider the following function. √x, (1, 1) (a) Find an equation of the tangent line to the graph of f at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. 2- y 1- -1 FK KE 2- y 1- 3 4 5 -1 0 1 O -1 -1 y y 3 2 1- 0 2- 1 2 1 2 2 3 4 4 5
Consider the following function. √x, (1, 1) (a) Find an equation of the tangent line to the graph of f at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. 2- y 1- -1 FK KE 2- y 1- 3 4 5 -1 0 1 O -1 -1 y y 3 2 1- 0 2- 1 2 1 2 2 3 4 4 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Topic: Tangent Lines and Graphical Representation
**Consider the following function:**
\[ \sqrt{x} \ , \quad (1, 1) \]
**(a)** Find an equation of the tangent line to the graph of \( f \) at the given point.
\[ y = \_\_\_\_\_\_ \]
**(b)** Use a graphing utility to graph the function and its tangent line at the point.
---
### Explanation of Graphs
The image contains four plots, each depicting the function \( y = \sqrt{x} \) along with a red tangent line. The graphs are laid out in a 2x2 grid:
1. **Top Left Graph:**
- The graph displays \( y = \sqrt{x} \) from \( x = -1 \) to about \( x = 5 \).
- The tangent line slightly differs in slopes as it goes through the point \( (1, 1) \).
2. **Top Right Graph:**
- Similarly structured, displaying \( y = \sqrt{x} \).
- The tangent line is drawn to emphasize the slope at point \( (1, 1) \), showing only a small discrepancy compared to the correct tangent.
3. **Bottom Left Graph:**
- Shows the curve \( y = \sqrt{x} \).
- Again, a red tangent line is placed, distinctly differing in slope.
4. **Bottom Right Graph:**
- Similar graph structure showing \( y = \sqrt{x} \).
- Depicts a correctly drawn tangent line indicating proper alignment with the point of tangency \( (1, 1) \).
A circle is placed underneath each graph, likely intended for selection purposes in an interactive setting.
These visualizations are intended to help students understand how the tangent line to the function \( \sqrt{x} \) can be represented graphically at the point \( (1, 1) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b6b3477-66d3-4452-8b0f-11f5e6ce06e0%2Ffc8ee6f0-9fdd-4663-85e2-832efb67d0c1%2Foedy894_processed.png&w=3840&q=75)
Transcribed Image Text:### Topic: Tangent Lines and Graphical Representation
**Consider the following function:**
\[ \sqrt{x} \ , \quad (1, 1) \]
**(a)** Find an equation of the tangent line to the graph of \( f \) at the given point.
\[ y = \_\_\_\_\_\_ \]
**(b)** Use a graphing utility to graph the function and its tangent line at the point.
---
### Explanation of Graphs
The image contains four plots, each depicting the function \( y = \sqrt{x} \) along with a red tangent line. The graphs are laid out in a 2x2 grid:
1. **Top Left Graph:**
- The graph displays \( y = \sqrt{x} \) from \( x = -1 \) to about \( x = 5 \).
- The tangent line slightly differs in slopes as it goes through the point \( (1, 1) \).
2. **Top Right Graph:**
- Similarly structured, displaying \( y = \sqrt{x} \).
- The tangent line is drawn to emphasize the slope at point \( (1, 1) \), showing only a small discrepancy compared to the correct tangent.
3. **Bottom Left Graph:**
- Shows the curve \( y = \sqrt{x} \).
- Again, a red tangent line is placed, distinctly differing in slope.
4. **Bottom Right Graph:**
- Similar graph structure showing \( y = \sqrt{x} \).
- Depicts a correctly drawn tangent line indicating proper alignment with the point of tangency \( (1, 1) \).
A circle is placed underneath each graph, likely intended for selection purposes in an interactive setting.
These visualizations are intended to help students understand how the tangent line to the function \( \sqrt{x} \) can be represented graphically at the point \( (1, 1) \).
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