a. if the marginal product is less than the average product, the average product is falling

Both the marginal product (MP) and average product (AP) curves are inverted U shaped curves. As marginal product goes on increasing, the average product is also rising, but less than marginal product. Then marginal product starts declining, but average product reaches maximum. After this point, average product starts falling, when marginal product is already declining, and becomes less than average product. This relationship we can see in the following diagram, at output level X*.

please see the attached file for the complete solution.