Which statements about the local maximums and minimums for the given function are true? check all that apply.

over the interval [–1, 1,] the local minimum is –8.
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.

A, C, D and E are true.

Step-by-step explanation:

According to the options, we have,

A. Over the interval [–1, 1,] the local minimum is –8.

We can see that the minimum point is (0.6,-8).

Thus, the local minimum is -8.

So, this is true.

B. Over the interval [1, 3], the local minimum is 0 .

We can see that the minimum point is (3.4,-8).

Thus, the local minimum is -8 and not 0.

So, this is false.

C. Over the interval [2, 4], the local minimum is –8.

We can see that the minimum point is (3.4,-8).

Thus, the local minimum is -8.

So, this is true.

D. Over the interval [3, 5], the local minimum is –8.

We can see that the minimum point is (3.4,-8).

Thus, the local minimum is -8.

So, this is true.

E. Over the interval [1, 4], the local maximum is 0.  

We can see that the maximum point is (2,0).

Thus, the local maximum is 0

So, this is true.

F. Over the interval [3, 5], the local maximum is 0.

We can see that there is no maximum point as the function tends to infinity.

So, this is false.

Hence, the statements which are true are,

A. Over the interval [–1, 1,] the local minimum is –8.

C. Over the interval [2, 4], the local minimum is –8.

D. Over the interval [3, 5], the local minimum is –8.

E. Over the interval [1, 4], the local maximum is 0.