The total revenue in rupees received from the sale of 'x' units of a product is given by:
`R(x)=13x^(2)+26x+20.`
Find the marginal revenue when x = 7

Answer

To find the marginal revenue when \( x = 7 \), we will follow these steps:

### Step 1: Understand the concept of Marginal Revenue
Marginal Revenue (MR) is defined as the derivative of the total revenue function \( R(x) \) with respect to \( x \). Mathematically, it is represented as:
\[ MR = \frac{dR}{dx} \]

### Step 2: Write down the total revenue function
The total revenue function given is:
\[ R(x) = 13x^2 + 26x + 20 \]

### Step 3: Differentiate the total revenue function
To find the marginal revenue, we need to differentiate \( R(x) \) with respect to \( x \):
\[ \frac{dR}{dx} = \frac{d}{dx}(13x^2) + \frac{d}{dx}(26x) + \frac{d}{dx}(20) \]

Calculating each term:
- The derivative of \( 13x^2 \) is \( 26x \) (using the power rule).
- The derivative of \( 26x \) is \( 26 \).
- The derivative of a constant \( 20 \) is \( 0 \).

Thus, we have:
\[ \frac{dR}{dx} = 26x + 26 \]

### Step 4: Substitute \( x = 7 \) into the marginal revenue function
Now we will find the marginal revenue when \( x = 7 \):
\[ MR = 26(7) + 26 \]

Calculating this gives:
\[ MR = 182 + 26 = 208 \]

### Conclusion
The marginal revenue when \( x = 7 \) is:
\[ \boxed{208} \text{ rupees per unit} \]

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