Questions: Find the marginal revenue function. R(x)=x(22-0.06 x) R'(x)=

Transcript text: Find the marginal revenue function. \[ R(x)=x(22-0.06 x) \] \[ R^{\prime}(x)= \]

Solution

Solution Steps

Step 1: Expand the Revenue Function

The given revenue function is: \[ R(x) = x(22 - 0.06x) \] First, expand the function: \[ R(x) = 22x - 0.06x^2 \]

Step 2: Differentiate the Revenue Function

To find the marginal revenue function \( R'(x) \), differentiate \( R(x) \) with respect to \( x \): \[ R'(x) = \frac{d}{dx}(22x - 0.06x^2) \] Using the power rule for differentiation: \[ R'(x) = 22 - 0.12x \]

Final Answer

The marginal revenue function is: \[ \boxed{R'(x) = 22 - 0.12x} \]

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