How can you figure out the local minimum, local maximum, constant, and neither to the following statements?

Suppose f (1) = 5 and f' (1) = 0. What can we conclude about the point (1, 5) if:

1. f' (x) < 0 for x < 1, and f' (x) > 0 for x > 1?

2. f' (x) < 0 for x < 1, and f' (x) < 0 for x > 1?

3. f' (x) > 0 for x < 1, and f' (x) < 0 for x > 1?

4. f' (x) > 0 for x < 1, and f' (x) > 0 for x > 1?

Local Minimum

Neither

Local Maximum

Constant