
Which statement is true about the local minimum of the graphed function?

Over the interval [–4, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 25.
Over the interval [–1, 4], the local minimum is 0.
Over the interval [4, 7], the local minimum is -7.


To determine which statement is true about the local minimum of the graphed function, we need to analyze the intervals and the given minimum values. Here’s the step-by-step approach:

1. **Interval [-4, -2], local minimum 0:** This suggests the function reaches a minimum value of 0 between -4 and -2. If the graph of the function indeed dips to 0 in this interval, this statement would be true. Otherwise, it's false.
  
2. **Interval [-2, -1], local minimum 25:** This implies that between -2 and -1, the function has a minimum value of 25. For this to be true, the graph should not dip below 25 in this range. Otherwise, it's false.

3. **Interval [-1, 4], local minimum 0:** In this interval, the function must reach a minimum value of 0 at some point between -1 and 4. If the function reaches this minimum, this statement is true.

4. **Interval [4, 7], local minimum -7:** This implies that the function reaches a minimum of -7 between 4 and 7. If the graph hits or goes to -7 in this range, the statement is true.

Since you mentioned this is based on a graphed function, I would need the specific graph to verify these statements precisely. Without the graph, it is hard to say definitively which statement is true. However, if we assume typical behavior of functions and these intervals, we could hypothesize based on a standard behavior (such as quadratic, cubic, etc.). 

Do you want to provide more details, or can you share the graph?

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Here are 5 related questions to explore further:
1. What is the definition of a local minimum for a function?
2. How can we determine the local minimum of a function using calculus (first and second derivative tests)?
3. Can a function have more than one local minimum over its entire domain?
4. How do the properties of a graph change at a local minimum point?
5. What tools can we use to approximate local minimum points from a graphed function?

**Tip:** When analyzing a graph for local minima, observe where the slope of the function changes from negative to positive. This indicates a local minimum point.

Which statement is true about the local minimum of the graphed function?
Over the interval [–4, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 25.
Over the interval [–1, 4], the local minimum is 0.
Over the interval [4, 7], the local minimum is -7.

Explore how to determine the local minimum of a graphed function over specific intervals like [–4, –2] and [4, 7]. This problem covers key mathematical concepts such as local minima and the derivative test for local extrema. Suitable for high school students in Grades 9-12.

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