Answer:
ii) Over the interval [2, 4], the local minimum is at -8
iii) Over the interval [3, 5], the local minimum is at -8
iv) Over the interval [1, 4], the local maximum is at 0
Step-by-step explanation:
The graph of the function is attached below.
The local minimum is the minimum point within a specified range while the local maximum is the maximum within a specified range.
i) We can see from the graph that within [1, 3] the local minimum is at -6, hence the first option is wrong.
ii) Over the interval [2, 4], the local minimum is at -8, hence option 2 is correct
iii) Over the interval [3, 5], the local minimum is at -8, hence option 3 is correct
iv) Over the interval [1, 4], the local maximum is at 0, hence option 3 is correct
v) Over the interval [3, 5], the local maximum is at infinity, hence option 5 is not correct
