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The image you provided contains a question involving the calculation of marginal cost (MC) using calculus, as well as the use of the total cost function \( C(x) \). Let me transcribe the relevant details to provide a solution.

### Problem Details:
1. **Given Cost Function:**
   \[
   C(x) = 8.3x^2 - 10x + 122
   \]

2. **Objective:**
   Find the marginal cost, \( MC \), which is the derivative of the total cost function \( C(x) \) with respect to \( x \).

### Steps to Solve:

1. **Differentiate the Cost Function:**
   To find the marginal cost, differentiate \( C(x) \) with respect to \( x \):
   \[
   MC(x) = \frac{d}{dx} \left( 8.3x^2 - 10x + 122 \right)
   \]

2. **Compute the Derivative:**
   - The derivative of \( 8.3x^2 \) is \( 2 \times 8.3x = 16.6x \).
   - The derivative of \( -10x \) is \( -10 \).
   - The derivative of the constant \( 122 \) is \( 0 \).

   Therefore, the marginal cost function is:
   \[
   MC(x) = 16.6x - 10
   \]

3. **Evaluate the Marginal Cost at Specific Values of \( x \):**
   You may be asked to evaluate the marginal cost at specific production levels (values of \( x \)), for example, \( x = 3 \), \( x = 5 \), etc.

### Do you want further details on this solution, or do you have any additional questions?

#### 5 Relative Questions:
1. What does the marginal cost function represent in the context of production?
2. How would you find the total cost of producing a specific number of units?
3. Can you explain the significance of the constant term in the cost function?
4. How does the marginal cost change as the production level increases?
5. What other economic interpretations can be derived from the marginal cost function?

#### Tip:
When differentiating a polynomial function, remember to apply the power rule, which states that the derivative of \( ax^n \) is \( n \times ax^{n-1} \).

Given the cost function C(x) = 8.3x^2 - 10x + 122, calculate the marginal cost (MC) by differentiating the function.

Learn how to calculate the marginal cost (MC) by differentiating the total cost function C(x) = 8.3x^2 - 10x + 122. This solution explains key calculus concepts and the power rule, suitable for college-level economics or calculus students.

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