At 1.5 the average total cost is a minimum and the total cost will be 10.25 where the TC = total cost; x = output (in 1,000 units)
Maxima and minima of a function are the extremes within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We have a total cost function:
TC = x³/3 - x² + 11x
Average total cost:
[tex]\rm F\left(x\right)=\dfrac{\left(\dfrac{x}{3}^3-\:x^2\:+\:11x\right)}{x}[/tex]
Differentiating with respect to x and equating to x
d(F(x))/dx = 0
We will get:
x = 1.5
F'(1.5) > 0
At 1.5 the average total cost is a minimum.
Thus, at 1.5 the average total cost is a minimum and the total cost will be 10.25 where the TC = total cost; x = output (in 1,000 units)
Learn more about the maxima and minima here:
brainly.com/question/6422517
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