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To find the average cost function, given the cost function \( C(x) = 122 + 6.2x \), we use the following formula for the average cost function:

\[
\overline{C}(x) = \frac{C(x)}{x}
\]

Now, substitute \( C(x) = 122 + 6.2x \) into the formula:

\[
\overline{C}(x) = \frac{122 + 6.2x}{x}
\]

Simplify the expression:

\[
\overline{C}(x) = \frac{122}{x} + 6.2
\]

Thus, the average cost function is:

\[
\overline{C}(x) = \frac{122}{x} + 6.2
\]

Would you like any further explanation on this or additional details on the steps?

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Here are 5 related questions for further exploration:
1. How does the average cost function change as \( x \) increases?
2. What is the behavior of \( \overline{C}(x) \) as \( x \to \infty \)?
3. What is the marginal cost of the given cost function?
4. How is the revenue function \( R(x) \) related to the cost function in profit analysis?
5. How would you compute the break-even point using \( C(x) \) and \( R(x) \)?

**Tip:** The average cost function helps identify the cost per unit, and it typically decreases as production increases, due to fixed costs being spread over more units.

Find the average cost function if cost and revenue are given by C(x) = 122 + 6.2x and R(x) = 7x - 0.09x^2.

Learn how to find the average cost function when given the cost function C(x) = 122 + 6.2x. This involves dividing the total cost function by the number of units, x, to calculate the cost per unit. Suitable for high school students in Grades 10-12.

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