# Deriving marginal cost function using first order derivative

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A firm has determined that its variable costs are given by the following relationship:

VC = .05Q3 - 5Q2 + 500Q

where Q is the quantity of output produced. The average variable cost function: AVC = .05Q2 - 5Q + 500. Determine the marginal cost function.

a. MC = .15Q2 - 10Q + 500

b. MC = .15Q4 - 10Q3 + 500Q2

c. MC = .05Q2 - 5Q + 500

d. MC = .05Q4 - 5Q3 + 500Q

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#### Solution Preview

A firm has determined that its variable costs are given by the following relationship:

VC = .05Q3 - 5Q2 + ...

#### Solution Summary

Using first order derivative how to get marginal cost function from average variable cost function.

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