Expression for Marginal Function M and Average Function A:
To find the expression for the marginal function (M) and average function (A), we need to first understand their definitions and relationships with the total function (T).

The total function (T) represents the total value or quantity of a certain variable (e.g., product or cost) as a function of another variable (e.g., input or output). Let's assume T is a function of X.

The marginal function (M) represents the rate of change of the total function with respect to the variable X. It measures the increase or decrease in the total function for a small change in X. Mathematically, it is expressed as:

M = dT/dX

The average function (A) represents the average value of the total function over a certain range of the variable X. It is calculated by dividing the total value of the function by the range of X. Mathematically, it is expressed as:

A = T/X

Relationship between M and A:
To understand the relationship between the marginal function (M) and the average function (A), let's consider the scenario where the average function reaches a relative extremum.

When the average function reaches a relative extremum, it means that the average value of the total function is either at a maximum or minimum within a certain range of X. In other words, the average rate of change of the total function is either at its highest or lowest point.

At this extremum point, the marginal function (M) is equal to zero. This is because the marginal function measures the rate of change of the total function, and at the extremum point, the rate of change is neither increasing nor decreasing. Therefore, we have M = 0.

Since M = 0, it implies that the average function (A) also equals zero at the extremum point. This means that the average value of the total function is equal to zero when the rate of change is neither increasing nor decreasing.

General Principle for Drawing Marginal and Average Curves:
Based on the relationship between M and A, the general principle for drawing marginal and average curves in the same diagram is as follows:

- The marginal curve should intersect the horizontal axis (X-axis) at the point where the average curve reaches a relative extremum.
- At this point, both the marginal and average values are zero.
- The marginal curve should be above the average curve when the average value is increasing and below the average curve when the average value is decreasing.

By following this principle, we can visually represent the relationship between the marginal and average functions on the same diagram.

Elasticity of the Total Function at Extreme Values of A:
When the average function (A) reaches an extreme value, it implies that the average rate of change of the total function is either at its highest or lowest point within a certain range of X.

The elasticity of the total function at the extreme value of A can be determined based on the slope of the total function at that point. If the slope is positive, it indicates that the total function is elastic, meaning that a small change in X leads to a relatively larger change in T. Conversely, if the slope is negative, it indicates that the total function is inelastic, meaning that a small change in X leads to a relatively smaller change in T.

Therefore, when the average function reaches an extreme value