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(Steps Shown) ACME office furniture maker has the daily cost function for making desk as follows C(x)=0.0002x^3-0.06x^2+100x+1000 Find the marginal cost

Question: ACME office furniture maker has the daily cost function for making desk as follows

\[C(x)=0.0002{{x}^{3}}-0.06{{x}^{2}}+100x+1000\]
  1. Find the marginal cost function
  2. Find the marginal cost when \[x=200\] and interpret your result.
  3. Assume that ACME office furniture estimated that total cost for making desk is \[C(x)=400+2x\]

Find the average cost function \[\bar{C}\] and find the marginal average cost function \[\bar{C}'\]

What happens to \[\bar{C}(x)\] when \[x\] is very large? Interpret your results

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