a) Assume current production is 80: c(80)=5148 monthly cost.
b) c(83)-c(80)=387.165 or 387.17 additional cost.
c) c(81)=5274.475, so marginal cost is 5274.475-5148=126.48.
If, however, we use calculus to calculate the rate of change, we differentiate: c'(x)=0.015x²+0.14x+18 and put x=80. This gives us 125.20 instead of 126.48.
d) If the marginal cost at x=80 is 126.475, then at x=82 the additional cost would be twice this at 252.95. If we use the calculus figure the additional cost would be 250.40.
e) Prediction for c(82)=5148+252.95=5400.95, or 5148+250.40=5398.40 if we use the calculus figure.
My guess is that you’re supposed to use the non-calculus figure (precalculus method).