The marginal cost of a product is modeled by $\frac { d C } { d x } = \frac { 8 } { \sqrt { x + 1 } }$ , when x = 8, C = 40. Find the cost function.
A) $C ( x ) = 8 \sqrt { x + 1 } + - 8$
B) $C ( x ) = 16 ( x + 1 ) + - 6$
C) $C ( x ) = 16 \sqrt { x + 1 } + - 8$
D) $C ( x ) = 8 \sqrt { x + 1 } + - 8$.
E) $C ( x ) = 8 ( x + 1 ) + - 6$

Question

Quizplus · Accepted Answer

To find the cost function, we need to integrate the marginal cost function.$$\int \frac { d C } { d x } = \int \frac { 8 } { \sqrt { x + 1 } } dx$$$$C(x) = 16\sqrt{x+1} + C$$Using the given condition, C(8) = 40, we can solve for the constant C:$$40 = 16\sqrt{8+1} + C$$$$40 = 16\sqrt{9} + C$$$$40 = 16(3) + C$$$$40 = 48 + C$$$$C = -8$$Therefore, the cost function is:$$C(x) = 16\sqrt{x+1} - 8$$

The Marginal Cost of a Product Is Modeled By dCdx=8x+1\frac { d C } { d x } = \frac { 8 } { \sqrt { x + 1 } }dxdC​=x+1​8​

The Marginal Cost of a Product Is Modeled By $\frac { d C } { d x } = \frac { 8 } { \sqrt { x + 1 } }$