C=2500+70x - 0.1x^2
C' = 70-0.2x
C'(71) = 70-0.2(71) = 70-14.2 = $55.80 for and estimate of the cost of the 71st food processor
Or you could calculate it exactly by finding C(71) - C(70). Find the total cost of 71
and subtract the total cost of 70
You can see the 2500 will cancel. It's the fixed cost = FC=2500. 70x-0.1x^2 = VC
C(71)-C(70) = VC(71) - VC(70) = 70(71)-0.1(71)^2 - 70(70)+ 0.1(70)^2 =
4970 - 0.1(5041) - 4900 +0.1(4900) = 70-0.01(141) =70-14.1 = $55.90 for cost of 71st processor
There's a dime difference between the estimate and the exact marginal cost
the estimate is the cost at a point. the exact MC is the cost over an interval of one unit