The following table gives a partial set of values of a polynomial function. x | -2 | -1 | 0 | 1 | 2 | 3
g(x) |-14| -2 | 0 |-4| -6| 2

Between which two values would a relative minimum most likely occur?

-2 and 0
-1 and 1
0 and 2
1 and 3

(-2 and 0 is incorrect btw)

Using the concepts of relative minimum and relative maximum, it is found that a relative minimum is most likely to occur between 1 and 3.

A relative minimum occurs when the function is decreasing, then it starts to increase.A relative maximum occurs when the function is increasing, then it starts to decrease.Over the interval -2 and 0, the function is increasing the whole time, which means that a relative minimum is not likely to occur.Over the interval -1 and 1, the function is increasing, then it starts to decrease, which means that a relative maximum is likely to occur.Over the interval 0 and 2, the function is decreasing the whole time, which means that a relative minimum is not likely to occur.Over the interval 1 and 3, the function is decreasing, then it starts to increase, which means that a relative minimum is likely to occur. This is the correct option.

A similar problem is given at