The statements about the local maximums and minimums for the given function which are true include:
- 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.
This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.
According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.
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