To analyze the graphed function and determine the local minimums and maximums, we need to consider the intervals given and identify which points on the graph fit the criteria for local extrema in those intervals.
The function has:
- Local minimum values at (0.6, -8) and (3.4, -8)
- A local maximum value at (2, 0)
- It crosses the x-axis at (0, 0), (2, 0), and (4, 0)
- It crosses the y-axis at (0, 0)
1. **Over the interval \([1, 3]\), the local minimum is 0:**
- This statement is **false**. There is no local minimum of 0 in this interval. Instead, there is the local maximum of 0 at \(x = 2\), but no local minimum of 0.
2. **Over the interval \([2, 4]\), the local minimum is –8:**
- This statement is **true**. The local minimum value of -8 occurs at \(x = 3.4\), which lies within the interval [2, 4].
3. **Over the interval \([3, 5]\), the local minimum is –8:**
- This statement is **true**. The local minimum value of -8 at \(x = 3.4\) is within the interval [3, 5].
4. **Over the interval \([1, 4]\), the local maximum is 0:**
- This statement is **true**. The local maximum value of 0 occurs at \(x = 2\), which is within the interval [1, 4].
5. **Over the interval \([3, 5]\), the local maximum is 0:**
- This statement is **false**. There is no local maximum of 0 in the interval [3, 5]. The only significant local value in this interval is the local minimum of -8 at \(x = 3.4\).
Hence, the three true statements about the local maximums and minimums for the given function are:
1. Over the interval \([2, 4]\), the local minimum is –8.
2. Over the interval \([3, 5]\), the local minimum is –8.
3. Over the interval \([1, 4]\), the local maximum is 0.
Analyze the graphed function to find the local minimum and the local maximum for the given function.
On a coordinate plane, a curved line with minimum values of (0.6, negative 8) and (3.4, negative 8), and a maximum value of (2, 0), crosses the x-axis at (0, 0), (2, 0), and (4, 0), and crosses the y-axis at (0, 0).
Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
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