If the marginal revenue (MR) is `9-6x^(2)+2x`, then revenue function is

Options

A. `9x+x^(2)-2x^(3)`
B. `9x+x^(2)+2x^(3)`
C. `9x-x^(2)+2x^(3)`
D. none of the above

Answer

To find the revenue function \( R(x) \) from the given marginal revenue \( MR = 9 - 6x^2 + 2x \), we will integrate the marginal revenue function with respect to \( x \).

### Step-by-Step Solution:

1. **Identify the Marginal Revenue Function**:
\[ MR = 9 - 6x^2 + 2x \]

2. **Set Up the Integral**:
To find the revenue function \( R(x) \), we need to integrate the marginal revenue function:
\[ R(x) = \int (9 - 6x^2 + 2x) \, dx \]

3. **Integrate Each Term**:
- The integral of \( 9 \) with respect to \( x \) is \( 9x \).
- The integral of \( -6x^2 \) is \( -6 \cdot \frac{x^3}{3} = -2x^3 \).
- The integral of \( 2x \) is \( 2 \cdot \frac{x^2}{2} = x^2 \).

Putting these together, we have:
\[ R(x) = 9x - 2x^3 + x^2 + C \]
where \( C \) is the constant of integration.

4. **Final Revenue Function**:
Thus, the revenue function is:
\[ R(x) = 9x - 2x^3 + x^2 + C \]