Question

Find the companies total cost function of the C’(x)=6x-7 and it’s fixed cost is $7

Answer 1

Answer:

Step-by-step explanation:
`\begin{gathered} C^(\prime)(x)\text{ = 6x - 7} \\ Fixed\text{ cost = \$7} \\ \\ We\text{ need to find the cost function by integrating the marginal cost function} \end{gathered}`
`\begin{gathered} \int C^(\prime)(x)\text{ = }\int(6x\text{ - 7\rparen dx} \\ C(x)\text{ = }\int6xdx\text{ - }\int7dx \\ C(x)\text{ = }(6x^2)/(2)-\text{ 7x +}C \\ C(x)\text{ = 3x}^2\text{ - 7x + }C \end{gathered}`

To get the value of the constant, we will equate the cost function to zero and substitute x with the fixed cost

`\begin{gathered} C(x)\text{ = 7 when x = 0} \\ 7\text{ = 3x}^2\text{ - 7x + }C \\ 7\text{ = 3\lparen0\rparen}^2\text{ -7\lparen0\rparen +C} \\ 7\text{ = C} \end{gathered}`

Substitute the value of C in the function of C(x) to get the total cost function:

`C(x)\text{ = 3x}^2\text{ - 7x + 7 \lparen option A\rparen}`