Find expert answers and community insights on IDNLearn.com. Join our interactive Q&A community and get reliable, detailed answers from experienced professionals across a variety of topics.
Sagot :
To determine the ordered pair closest to a local minimum of the function [tex]\( f(x) \)[/tex], we need to analyze the given points. Here we have the following points:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -2 & -8 \\ \hline -1 & -3 \\ \hline 0 & -2 \\ \hline 1 & 4 \\ \hline 2 & 1 \\ \hline 3 & 3 \\ \hline \end{array} \][/tex]
Let's examine the behavior of the function [tex]\( f(x) \)[/tex] at each point:
1. [tex]\( f(-2) = -8 \)[/tex]
2. [tex]\( f(-1) = -3 \)[/tex]
3. [tex]\( f(0) = -2 \)[/tex]
4. [tex]\( f(1) = 4 \)[/tex]
5. [tex]\( f(2) = 1 \)[/tex]
6. [tex]\( f(3) = 3 \)[/tex]
We look for a local minimum in a function by checking if the value at a certain point is lower than its neighboring points.
For the given values, let's evaluate the ordered pairs:
1. Between [tex]\( x = -2 \)[/tex] and [tex]\( x = -1 \)[/tex], [tex]\( f(x) \)[/tex] increases from -8 to -3.
2. Between [tex]\( x = -1 \)[/tex] and [tex]\( x = 0 \)[/tex], [tex]\( f(x) \)[/tex] increases from -3 to -2.
3. Between [tex]\( x = 0 \)[/tex] and [tex]\( x = 1 \)[/tex], [tex]\( f(x) \)[/tex] decreases from -2 to 4.
4. Between [tex]\( x = 1 \)[/tex] and [tex]\( x = 2 \)[/tex], [tex]\( f(x) \)[/tex] decreases from 4 to 1.
5. Between [tex]\( x = 2 \)[/tex] and [tex]\( x = 3 \)[/tex], [tex]\( f(x) \)[/tex] increases from 1 to 3.
The point [tex]\( (0, -2) \)[/tex] presents an interesting case where it is surrounded by higher values on both sides. This indicates a local minimum within our given range.
Thus, the ordered pair closest to a local minimum of the function [tex]\( f(x) \)[/tex] is:
[tex]\[ (0, -2) \][/tex]
So, from the given choices, the ordered pair closest to a local minimum of the function [tex]\( f(x) \)[/tex] is:
[tex]\[ (0, -2) \][/tex]
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -2 & -8 \\ \hline -1 & -3 \\ \hline 0 & -2 \\ \hline 1 & 4 \\ \hline 2 & 1 \\ \hline 3 & 3 \\ \hline \end{array} \][/tex]
Let's examine the behavior of the function [tex]\( f(x) \)[/tex] at each point:
1. [tex]\( f(-2) = -8 \)[/tex]
2. [tex]\( f(-1) = -3 \)[/tex]
3. [tex]\( f(0) = -2 \)[/tex]
4. [tex]\( f(1) = 4 \)[/tex]
5. [tex]\( f(2) = 1 \)[/tex]
6. [tex]\( f(3) = 3 \)[/tex]
We look for a local minimum in a function by checking if the value at a certain point is lower than its neighboring points.
For the given values, let's evaluate the ordered pairs:
1. Between [tex]\( x = -2 \)[/tex] and [tex]\( x = -1 \)[/tex], [tex]\( f(x) \)[/tex] increases from -8 to -3.
2. Between [tex]\( x = -1 \)[/tex] and [tex]\( x = 0 \)[/tex], [tex]\( f(x) \)[/tex] increases from -3 to -2.
3. Between [tex]\( x = 0 \)[/tex] and [tex]\( x = 1 \)[/tex], [tex]\( f(x) \)[/tex] decreases from -2 to 4.
4. Between [tex]\( x = 1 \)[/tex] and [tex]\( x = 2 \)[/tex], [tex]\( f(x) \)[/tex] decreases from 4 to 1.
5. Between [tex]\( x = 2 \)[/tex] and [tex]\( x = 3 \)[/tex], [tex]\( f(x) \)[/tex] increases from 1 to 3.
The point [tex]\( (0, -2) \)[/tex] presents an interesting case where it is surrounded by higher values on both sides. This indicates a local minimum within our given range.
Thus, the ordered pair closest to a local minimum of the function [tex]\( f(x) \)[/tex] is:
[tex]\[ (0, -2) \][/tex]
So, from the given choices, the ordered pair closest to a local minimum of the function [tex]\( f(x) \)[/tex] is:
[tex]\[ (0, -2) \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thanks for visiting IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more helpful information.