At the point of inflection, the marginal product is maximum. Let's understand this concept in detail:

1. Introduction
In economics, the production function describes the relationship between inputs used in production (such as labor and capital) and the output produced. The production function can be represented mathematically as Q = f(L,K), where Q is the output, L is the quantity of labor, and K is the quantity of capital.

2. Total Product (TP)
Total product refers to the total quantity of output produced by a given combination of inputs. It represents the entire output produced by a firm.

3. Average Product (AP)
Average product refers to the output produced per unit of input. It is calculated by dividing the total product by the quantity of input used. AP = TP / input.

4. Marginal Product (MP)
Marginal product refers to the additional output produced by using one additional unit of input while keeping other inputs constant. It is calculated by taking the derivative of the total product with respect to the input. MP = dTP / dinput.

5. Point of Inflexion
The point of inflection occurs where the slope of the marginal product curve changes sign. At this point, the marginal product is neither increasing nor decreasing but reaches its maximum value.

6. Relationship between Marginal Product and Average Product
The average product is equal to the marginal product when the average product is at its maximum. This occurs when the marginal product curve intersects the average product curve at its peak.

7. Explanation of the Correct Answer
At the point of inflection, the marginal product is maximum. This means that the additional output produced by using one additional unit of input is at its highest point. It signifies that the firm is experiencing diminishing returns to inputs beyond this point.

Conclusion
In summary, the correct answer is option 'B' - at the point of inflection, the marginal product is maximum. This concept is important in understanding the relationship between inputs and outputs in production and helps firms optimize their production processes.