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MC = 125 - 0.42Q + 0.0021Q^2

Given the estimated marginal cost function, what are the total, variable, and average cost functions?

At what output level does AVC reach its minimum value in the long run? What is the value of AVC at its minimum point?

MC is the first derivitive of the total cost function. So, pretend you are integrating.
TC = 125Q + (.42/2)Q^2 + (.0021/3)Q^3

Divide by Q to get AVC.

Use standard calculus to find the minima of the AVC function.

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