Use the given graph of the function on the interval (0,8] to answer the following questions.
Where does the function f have a local maximum?
Answer (separate by commas): x=
Where does the function f have a local minimum?
What is the global maximum of f?
What is the global minimum of f?
given??
To determine the local maximum and minimum of the function f on the interval (0,8], we need to locate the highest and lowest points within that interval on the graph.
Based on the given graph, we can identify the following:
1. Local Maximum: The local maximum occurs at the point where the graph reaches its highest peak within the interval (0,8]. In this case, the local maximum occurs at x = 6.
2. Local Minimum: The local minimum occurs at the point where the graph reaches its lowest dip within the interval (0,8]. In this case, there is no local minimum within the given interval.
3. Global Maximum: The global maximum of a function refers to the highest point on the entire graph, not just within a specific interval. Since the graph is only given for the interval (0,8], we cannot determine the global maximum based on the information provided.
4. Global Minimum: Similarly, the global minimum of a function refers to the lowest point on the entire graph. Since the graph is only given for the interval (0,8], we cannot determine the global minimum based on the information provided.
Please note that to accurately determine the global maximum and minimum, we would need the graph for the entire domain of the function.
To answer these questions, you need to understand the concept of local and global extrema in a function and how to identify them using a graph. Here's how you can find the answers using the given graph:
1. Where does the function f have a local maximum?
A local maximum occurs when the function reaches its highest point within a specific interval. To find the local maximum on the graph, look for points where the graph reaches a peak and then starts decreasing on either side. In other words, identify the points where the graph changes from increasing to decreasing. Mark all the x-values where this happens, and list them as the local maxima.
2. Where does the function f have a local minimum?
A local minimum occurs when the function reaches its lowest point within a specific interval. To find the local minimum on the graph, look for points where the graph reaches a valley and then starts increasing on either side. In other words, identify the points where the graph changes from decreasing to increasing. Mark all the x-values where this happens, and list them as the local minima.
3. What is the global maximum of f?
The global maximum is the highest point on the entire graph, regardless of any specific interval. To find the global maximum, examine the entire graph and identify the highest point. This point represents the global maximum.
4. What is the global minimum of f?
The global minimum is the lowest point on the entire graph, regardless of any specific interval. To find the global minimum, examine the entire graph and identify the lowest point. This point represents the global minimum.
By following these steps and examining the given graph, you should be able to find the answers to the questions about local and global extrema.