Question

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

Answer 1

B, C, D

Explanation:

Hope this helps!

Answer 2

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

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