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# Propose a second degree cost function and explain it $crossing points, F, Cv, concavity, etc.$

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## Answer to a math question Propose a second degree cost function and explain it $crossing points, F, Cv, concavity, etc.$

Bud
4.6
1. **Identify the Cost Function**:

Given the general form of a quadratic cost function:

C$x$ = ax^2 + bx + c

2. **Intercept with y-axis $Fixed Costs$**:

The term c represents the fixed costs $F$, where the cost function intersects the y-axis $i.e., when x = 0$.

C$0$ = c

3. **Variable Costs**:

The term bx corresponds to the variable costs $Cv$, where the cost increases linearly with the increase in production x.

C_{v}$x$ = bx

The term ax^2 shows the rate of change in cost with respect to production. The sign of a determines the concavity of the function:

- If a > 0, the function is concave up $U-shaped$, indicating increasing costs at increasing rates as production rises.
- If a < 0, the function is concave down $∩-shaped$, indicating increasing costs at decreasing rates as production rises.

5. **Break-even Points**:

Solving for the points where the cost function intersects the x-axis $break-even points$ by setting C$x$ = 0 and solving the quadratic equation:

ax^2 + bx + c = 0

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

C$x$ = ax^2 + bx + c
Frequently asked questions $FAQs$