Math  /  Calculus

Question16. [0/1 Points] DETAILS MY NOTES TANAPMATH7 9.8.006. PREVIOUS ANSWERS
Marginal Average Cost for Producing Thermometers The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing xx thermometers is represented by the following function. Find the following functions (in dollars) and interpret your results. C(x)=6,500+9xC(x)=6,500+9 x (a) Find the average cost function Cˉ\bar{C}. Cˉ(x)=\bar{C}(x)= \square (b) Find the marginal average cost function Cˉ\bar{C}^{\prime}. Cˉ(x)=\bar{C}^{\prime}(x)= \square (c) Interpret your results. Since the marginal average cost function is negative for x>0x>0, the rate of change of the average cost function is negative for all x>0x>0. Since the marginal average cost function is negative for x>0x>0, the rate of change of the average cost function is positive for all x>0x>0. Since the marginal average cost function is positive for x>0x>0, the rate of change of the average cost function is negative for all x>0x>0. Since the marginal average cost function is positive for x>0x>0, the rate of change of the average cost function is positive for all x>0x>0. Submit Answer

Studdy Solution
Interpret the results:
Since Cˉ(x)=6,500x2\bar{C}^{\prime}(x) = -\frac{6,500}{x^2} is negative for x>0x > 0, the rate of change of the average cost function is negative for all x>0x > 0.
Thus, the correct interpretation is:
"Since the marginal average cost function is negative for x>0x > 0, the rate of change of the average cost function is negative for all x>0x > 0."
The functions and interpretation are as follows:
(a) Cˉ(x)=6,500x+9\bar{C}(x) = \frac{6,500}{x} + 9
(b) Cˉ(x)=6,500x2\bar{C}^{\prime}(x) = -\frac{6,500}{x^2}
(c) "Since the marginal average cost function is negative for x>0x > 0, the rate of change of the average cost function is negative for all x>0x > 0."

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