Marginal product and inflexion point:

Marginal product refers to the additional output produced by adding one more unit of input. In other words, it is the increase in production resulting from the addition of one more unit of input.

Inflexion point refers to the point on a graph where the curve changes from being concave upwards to concave downwards or vice versa. It is the point where the second derivative of the function changes sign.

Marginal product and inflexion point are related because the marginal product curve is the first derivative of the production function, and the inflexion point is where the second derivative of the production function changes sign.

Answer:

At the point of inflexion, the marginal product is maximum. This is because the point of inflexion is where the marginal product curve changes from increasing to decreasing. Before the inflexion point, the marginal product is increasing, and after the inflexion point, it is decreasing.

Therefore, the maximum point of the marginal product curve corresponds to the inflexion point of the production function. At this point, the firm is producing output most efficiently, and any further increase in input will result in a decrease in marginal product.

In summary, the inflexion point of the production function is where the marginal product is maximum. This is because it is the point where the marginal product curve changes from increasing to decreasing.