Solve the inequality f(x) ≥ 0, where f(x) = 2(x + 2)(x-3), by using the graph of the function. Q -6 -4 160- 120- 80- 40- -40- -80- ·1294 -160- 4 D The solution set for f(x) 20 is (Type your answer in interval notation.)
Solve the inequality f(x) ≥ 0, where f(x) = 2(x + 2)(x-3), by using the graph of the function. Q -6 -4 160- 120- 80- 40- -40- -80- ·1294 -160- 4 D The solution set for f(x) 20 is (Type your answer in interval notation.)
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
![**Solving the Inequality Using Graphs**
**Problem Statement:**
Solve the inequality \( f(x) \geq 0 \), where \( f(x) = 2(x + 2)(x - 3)^3 \), by using the graph of the function.
**Graph Explanation:**
- The graph of the function \( f(x) \) is a curve that intersects the x-axis at \( x = -2 \) and \( x = 3 \).
- The graph is a cubic function multiplied by a linear function.
- The x-axis represents the values of \( x \) and the y-axis represents the values of \( f(x) \).
- The curve has turning points and changes direction at certain intervals.
**Observations from the Graph:**
1. The function \( f(x) \) is positive or zero at:
- \( x \leq -2 \): The portion of the graph to the left of \( x = -2 \) goes upwards and is above the x-axis.
- \( x \in [3, \infty) \): The portion of the graph to the right of \( x = 3 \) goes upwards and is above the x-axis.
2. The function \( f(x) \) is negative between \( x = -2 \) and \( x = 3 \).
**Solution:**
The solution set for \( f(x) \geq 0 \) is the union of the intervals where the function is non-negative.
Therefore, the solution set is:
\[ (-\infty, -2] \cup [3, \infty) \]
**Instruction:**
Please type your answer in interval notation:
\[ \boxed{(-\infty, -2] \cup [3, \infty)} \]
Use this information to solve similar graph-based inequalities by observing where the function crosses the x-axis and determining the intervals where the function is non-negative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F918808b3-3bab-4c24-a49a-fe439aaeecc0%2F14ae47e3-2e68-473c-aeca-3e36bed916d3%2Fs0aohbplq_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving the Inequality Using Graphs**
**Problem Statement:**
Solve the inequality \( f(x) \geq 0 \), where \( f(x) = 2(x + 2)(x - 3)^3 \), by using the graph of the function.
**Graph Explanation:**
- The graph of the function \( f(x) \) is a curve that intersects the x-axis at \( x = -2 \) and \( x = 3 \).
- The graph is a cubic function multiplied by a linear function.
- The x-axis represents the values of \( x \) and the y-axis represents the values of \( f(x) \).
- The curve has turning points and changes direction at certain intervals.
**Observations from the Graph:**
1. The function \( f(x) \) is positive or zero at:
- \( x \leq -2 \): The portion of the graph to the left of \( x = -2 \) goes upwards and is above the x-axis.
- \( x \in [3, \infty) \): The portion of the graph to the right of \( x = 3 \) goes upwards and is above the x-axis.
2. The function \( f(x) \) is negative between \( x = -2 \) and \( x = 3 \).
**Solution:**
The solution set for \( f(x) \geq 0 \) is the union of the intervals where the function is non-negative.
Therefore, the solution set is:
\[ (-\infty, -2] \cup [3, \infty) \]
**Instruction:**
Please type your answer in interval notation:
\[ \boxed{(-\infty, -2] \cup [3, \infty)} \]
Use this information to solve similar graph-based inequalities by observing where the function crosses the x-axis and determining the intervals where the function is non-negative.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 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,
