Find all critical values for f(x) = (x + 7)°(x + 3)°. The critical values occur at x = (Enter your answers separated by commas) Question Help: D Video 1 D Video 2 E Written Example 1 Add Work бх + 4 Find all critical values for f(x) 9x2 – 5x + 3 The critical values occur at x = (Enter your answers separated by commas) Question Help: D Video 1 D Video 2 B Written Example 1 Add Work Find the absolute maximum and absolute minimum of f(x) = x – 3x? - 72x – 18 over the interval %3D [- 1, 11] The absolute maximum over the interval [- 1, 11] will be which will occur at x = The absolute minimum over the interval [ - 1, 11] will be which will occur at x =
Find all critical values for f(x) = (x + 7)°(x + 3)°. The critical values occur at x = (Enter your answers separated by commas) Question Help: D Video 1 D Video 2 E Written Example 1 Add Work бх + 4 Find all critical values for f(x) 9x2 – 5x + 3 The critical values occur at x = (Enter your answers separated by commas) Question Help: D Video 1 D Video 2 B Written Example 1 Add Work Find the absolute maximum and absolute minimum of f(x) = x – 3x? - 72x – 18 over the interval %3D [- 1, 11] The absolute maximum over the interval [- 1, 11] will be which will occur at x = The absolute minimum over the interval [ - 1, 11] will be which will occur at x =
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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![### Educational Exercise on Finding Critical Values and Extreme Values
#### Problem 1
**Find all critical values for \( f(x) = (x+7)^9(x+3)^6 \).**
The critical values occur at \( x = \) ________ . (Enter your answers separated by commas)
**Question Help:**
- Video 1
- Video 2
- Written Example 1
**Add Work**
---
#### Problem 2
**Find all critical values for \( f(x) = \frac{6x + 4}{9x^2 - 5x + 3} \).**
The critical values occur at \( x = \) ________ . (Enter your answers separated by commas)
**Question Help:**
- Video 1
- Video 2
- Written Example 1
**Add Work**
---
#### Problem 3
**Find the absolute maximum and absolute minimum of \( f(x) = x^3 - 3x^2 - 72x - 18 \) over the interval \([-1,11]\).**
- The absolute maximum over the interval \([-1,11]\) will be ________ , which will occur at \( x = \) ________ .
- The absolute minimum over the interval \([-1,11]\) will be ________ , which will occur at \( x = \) ________ .
**Question Help:**
- Video 1
- Video 2
- Written Example 1
**Add Work**
---
#### Graphs and Diagrams
In this exercise, you are prompted to solve problems involving the calculation of critical values and determining absolute maximum and minimum points of given functions. Videos and written examples are provided to aid in understanding the topics better.
1. **Critical Values:** Critical values are found by setting the derivative of the function to zero or by determining where the derivative does not exist. Critical points are essential in locating relative maxima and minima.
2. **Extreme Values:** The absolute maximum and minimum values of a function over a closed interval can be found by evaluating the function at critical points and endpoints of the interval, then comparing the values.
In general, graphical illustrations and step-by-step video tutorials would guide you through the process of solving these problems, ensuring a comprehensive understanding of finding critical values and determining extreme values on specific intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5234ec62-d297-4730-b48b-49cc88e7375d%2F3c626672-0652-4cea-b03a-2163f4071f05%2Ffubcv2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Exercise on Finding Critical Values and Extreme Values
#### Problem 1
**Find all critical values for \( f(x) = (x+7)^9(x+3)^6 \).**
The critical values occur at \( x = \) ________ . (Enter your answers separated by commas)
**Question Help:**
- Video 1
- Video 2
- Written Example 1
**Add Work**
---
#### Problem 2
**Find all critical values for \( f(x) = \frac{6x + 4}{9x^2 - 5x + 3} \).**
The critical values occur at \( x = \) ________ . (Enter your answers separated by commas)
**Question Help:**
- Video 1
- Video 2
- Written Example 1
**Add Work**
---
#### Problem 3
**Find the absolute maximum and absolute minimum of \( f(x) = x^3 - 3x^2 - 72x - 18 \) over the interval \([-1,11]\).**
- The absolute maximum over the interval \([-1,11]\) will be ________ , which will occur at \( x = \) ________ .
- The absolute minimum over the interval \([-1,11]\) will be ________ , which will occur at \( x = \) ________ .
**Question Help:**
- Video 1
- Video 2
- Written Example 1
**Add Work**
---
#### Graphs and Diagrams
In this exercise, you are prompted to solve problems involving the calculation of critical values and determining absolute maximum and minimum points of given functions. Videos and written examples are provided to aid in understanding the topics better.
1. **Critical Values:** Critical values are found by setting the derivative of the function to zero or by determining where the derivative does not exist. Critical points are essential in locating relative maxima and minima.
2. **Extreme Values:** The absolute maximum and minimum values of a function over a closed interval can be found by evaluating the function at critical points and endpoints of the interval, then comparing the values.
In general, graphical illustrations and step-by-step video tutorials would guide you through the process of solving these problems, ensuring a comprehensive understanding of finding critical values and determining extreme values on specific intervals.
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