The total revenue received from the sale of x units of a product is given by `R(x) = 20 x - 0.5x^(2)`. Find
Marginal revenue

Answer

To find the marginal revenue from the total revenue function \( R(x) = 20x - 0.5x^2 \), we will follow these steps:

### Step 1: Write down the total revenue function
The total revenue function is given as:
\[ R(x) = 20x - 0.5x^2 \]

### Step 2: Differentiate the total revenue function
To find the marginal revenue, we need to differentiate the total revenue function \( R(x) \) with respect to \( x \). The marginal revenue \( MR \) is given by:
\[ MR = \frac{dR}{dx} \]

### Step 3: Apply the differentiation rules
Using the power rule of differentiation, where \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \), we differentiate each term in \( R(x) \):
- The derivative of \( 20x \) is \( 20 \).
- The derivative of \( -0.5x^2 \) is \( -0.5 \cdot 2x = -x \).

Putting it all together, we get:
\[ MR = \frac{dR}{dx} = 20 - x \]

### Step 4: State the final result
Thus, the marginal revenue is:
\[ MR = 20 - x \]