Questions: Find the marginal average cost function if cost and revenue are given by C(x)=119+7.6x and R(x)=3x-0.01x^2 The marginal average cost function is C'(x)=

Find the marginal average cost function if cost and revenue are given by C(x)=119+7.6x and R(x)=3x-0.01x^2

The marginal average cost function is C'(x)=

Transcript text: Find the marginal average cost function if cost and revenue are given by $C(x)=119+7.6 x$ and $R(x)=3 x-0.01 x^{2}$ The marginal average cost function is $\overline{\mathrm{C}}^{\prime}(\mathrm{x})=$ $\square$

Solution

Solution Steps

To find the marginal average cost function, we need to follow these steps:

Calculate the average cost function, which is $ \overline{C}(x) = \frac{C(x)}{x} $.
Differentiate the average cost function with respect to $ x $ to find the marginal average cost function.

Step 1: Define the Cost Function

The cost function is given by: \[ C(x) = 119 + 7.6x \]

Step 2: Calculate the Average Cost Function

The average cost function is: \[ \overline{C}(x) = \frac{C(x)}{x} = \frac{119 + 7.6x}{x} = 7.6 + \frac{119}{x} \]

Step 3: Differentiate the Average Cost Function

To find the marginal average cost function, we differentiate the average cost function with respect to $ x $: \[ \overline{C}'(x) = \frac{d}{dx} \left( 7.6 + \frac{119}{x} \right) = 0 - \frac{119}{x^2} = -\frac{119}{x^2} \]