a. Graph the function f(x)=x²-8x+12. b. Identify the point (a,f(a)) at which the function has a tangent line with zero slope. c. Confirm your answer to part (b) by making a table of slopes of secant lines to approximate the slope of the tangent line at this point. A. VZ B. b. The function has a tangent line with zero slope at (4,-4). (Type an ordered pair.) c. Complete the table below. (Type integers or decimals rounded to four decimal places as needed.) Interval Slope of the secant line 0.5 0.1 .01 .001 .0001 [4,4.5] [4,4.1] [4,4.01] [4,4.001] [4,4.0001] An accurate conjecture for the slope of the tangent line is (Type an integer or a decimal.) O C. o
a. Graph the function f(x)=x²-8x+12. b. Identify the point (a,f(a)) at which the function has a tangent line with zero slope. c. Confirm your answer to part (b) by making a table of slopes of secant lines to approximate the slope of the tangent line at this point. A. VZ B. b. The function has a tangent line with zero slope at (4,-4). (Type an ordered pair.) c. Complete the table below. (Type integers or decimals rounded to four decimal places as needed.) Interval Slope of the secant line 0.5 0.1 .01 .001 .0001 [4,4.5] [4,4.1] [4,4.01] [4,4.001] [4,4.0001] An accurate conjecture for the slope of the tangent line is (Type an integer or a decimal.) O C. o
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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I need help finding An accurate conjecture for the slope of the tangent line for part c
![### Analyzing and Approximating Tangent Lines
#### Instructions:
1. **Graphing the Function**
- Graph the function \( f(x) = x^2 - 8x + 12 \).
2. **Identifying the Tangent Line**
- Identify the point \((a, f(a))\) where the function has a tangent line with zero slope.
3. **Confirming the Tangent Slope**
- Confirm your answer for part (b) by creating a table of slopes of secant lines to approximate the slope of the tangent line at this point.
#### Solution:
##### Graph Examples:
- **Graph A**: This graph is a parabolic curve opening upwards.
- **Graph B**: This graph is a parabolic curve as well, centered in the middle but zoomed in.
- **Graph C**: This graph is another parabolic curve with a different scale.
**Selected Graph**: The correct graph for \( f(x) = x^2 - 8x + 12 \) is **Graph A**.
##### Tangent Line with Zero Slope:
- The function \( f(x) = x^2 - 8x + 12 \) has a tangent line with zero slope at the point \((4, -4)\).
##### Approximating the Slope of the Tangent Line:
To confirm this, the following table represents slopes of secant lines approaching the point \((4, -4)\).
| Interval | Slope of the Secant Line |
|-----------|--------------------------|
| [4, 4.5] | 0.5 |
| [4, 4.1] | 0.1 |
| [4, 4.01] | 0.01 |
| [4, 4.001]| 0.001 |
| [4, 4.0001]| 0.0001 |
As the intervals get smaller and approach \( x = 4 \), the slope of the secant lines get closer to 0.
**Accurate Conjecture for the Slope of the Tangent Line: \( {0} \)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f1b7c10-7ca4-413c-bb43-fe1a15020101%2F5b8d2e2a-fdf0-4a58-ac6f-431c9bbfc028%2Fcgcu4bn_processed.png&w=3840&q=75)
Transcribed Image Text:### Analyzing and Approximating Tangent Lines
#### Instructions:
1. **Graphing the Function**
- Graph the function \( f(x) = x^2 - 8x + 12 \).
2. **Identifying the Tangent Line**
- Identify the point \((a, f(a))\) where the function has a tangent line with zero slope.
3. **Confirming the Tangent Slope**
- Confirm your answer for part (b) by creating a table of slopes of secant lines to approximate the slope of the tangent line at this point.
#### Solution:
##### Graph Examples:
- **Graph A**: This graph is a parabolic curve opening upwards.
- **Graph B**: This graph is a parabolic curve as well, centered in the middle but zoomed in.
- **Graph C**: This graph is another parabolic curve with a different scale.
**Selected Graph**: The correct graph for \( f(x) = x^2 - 8x + 12 \) is **Graph A**.
##### Tangent Line with Zero Slope:
- The function \( f(x) = x^2 - 8x + 12 \) has a tangent line with zero slope at the point \((4, -4)\).
##### Approximating the Slope of the Tangent Line:
To confirm this, the following table represents slopes of secant lines approaching the point \((4, -4)\).
| Interval | Slope of the Secant Line |
|-----------|--------------------------|
| [4, 4.5] | 0.5 |
| [4, 4.1] | 0.1 |
| [4, 4.01] | 0.01 |
| [4, 4.001]| 0.001 |
| [4, 4.0001]| 0.0001 |
As the intervals get smaller and approach \( x = 4 \), the slope of the secant lines get closer to 0.
**Accurate Conjecture for the Slope of the Tangent Line: \( {0} \)**
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