Which interval contains a local minimum for the graphed function?
1 answer:
We define a local minimum as a point x₀ such that f(x₀) ≤ f(x) for any value of x in a given interval (a, b), such that x₀ also belong to that interval.
We will see that the only interval that contains a local minimum is [2.5, 4]
These are easier to identify in graphs, as we only need to see a low point where the function stops to decrease and starts to increases, these are local minimums.
In this graph we can see two, that are marked in the image below:
One is at (3, -4) and the other is at (-0.44, -4.3)
So the intervals that contain local minimums are (remember that we look to the values of x)
[2.5, 4]
This is the only interval that contains a local minimum (the second one).
If you want to learn more, you can read:
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