If the total cost function for a product is $C ( x ) = 200 + 4 x + 0.09 x ^ { 2 }$ dollars. Find the minimum average cost.
A) $\$ 15.00$
B) $\$ 23.00$
C) $\$ 13.03$
D) $\$ 12.49$
E) $\$ 11.00$

Question

Quizplus · Accepted Answer

The average cost (AC) function is found by dividing the total cost function $C(x)$ by the quantity $x$, so $AC(x) = \frac{C(x)}{x} = \frac{200 + 4x + 0.09x^2}{x}$. To find the minimum average cost, we differentiate the AC function with respect to $x$ and set the derivative equal to zero to solve for $x$. The derivative of AC with respect to $x$ gives us the rate of change of the average cost with respect to the quantity produced. Setting this derivative equal to zero and solving for $x$ will give us the quantity at which the average cost is minimized. After finding this quantity, we substitute it back into the AC function to find the minimum average cost.

If the Total Cost Function for a Product Is C(x)=200+4x+0.09x2C ( x ) = 200 + 4 x + 0.09 x ^ { 2 }C(x)=200+4x+0.09x2

If the Total Cost Function for a Product Is $C ( x ) = 200 + 4 x + 0.09 x ^ { 2 }$