This statement is not true. When marginal product is negative, total product is not increasing. It is possible for total product to increase at a decreasing rate, but in such cases, marginal product is still positive; it is only lower than it was for the previous unit.
For example, let us imagine that a firm makes 10 units of product with one worker. It adds another worker and makes 18 units, for a marginal product of 8. It adds a third worker and makes 23 units, for a marginal product of 5. This means that total product is increasing at a decreasing rate now, but the marginal product is still positive. Now let us imagine that the firm adds a fourth worker but that worker simply gets in the way while trying to help. Now the firm makes 22 units. Its marginal product is now negative 1. When marginal product is negative like this, the firm’s total output is actually going down. It is not increasing at all.
So, this statement is not true because any negative marginal product represents an actual decline in production.