Marginal Cost: From an Estimate to an Exact Change
Distinguish a marginal rate from an exact cost increase. Compare an estimate with a shaded-area graph, recover total cost by integration and explore average unit cost.
McGill University · MATH 122
McGill MATH 122 tutoring
Calculus for Management: one-to-one online tutoring and exam preparation.
Listed course
Course overview
McGill MATH 122 connects one-variable differential and integral calculus with business applications. The course reviews functions, develops limits and derivatives, then covers antiderivatives and definite integrals. Its official description excludes trigonometric functions.
Restricted to Desautels Faculty of Management students.
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MATH 122 topics to review
Functions in business applicationsExponents, radicals, exponentials and logarithmsLimits and continuityDifferentiation and applicationsAntiderivatives and definite integralsIntegration techniques and applications
Common difficulties
- Distinguishing total cost, average unit cost and marginal cost
- Choosing between a local estimate and an exact accumulated change
Preparing for this course
Review function notation, factoring, powers and logarithms. When calculus stalls, first check whether the obstacle is an algebraic step, a derivative rule or the meaning of a rate. The short question beside this note checks that last distinction.
Registration requirements
A course in functions is the listed prerequisite. Open only to Desautels Faculty of Management students. Prior or concurrent calculus restrictions apply; consult McGill for eligibility and the recommended route for a mathematics or statistics major or minor.
Check the official course catalogueMarginal cost: a rate or the exact cost of one more unit?
Let be the number of units produced, treated as a continuous variable on . The total cost, expressed in Canadian dollars (CAD), is . Find and its units. Does it give the exact cost of producing the 51st unit?
Show the reasoning
Differentiate and interpret the rate
The constant fixed cost disappears under differentiation: , so CAD per unit. This is the instantaneous rate of cost increase at a production level of 50 units.
Check the one-unit increase
The local estimate is CAD. The exact increase is CAD. Marginal cost, the instantaneous rate of change of total cost as production changes, rises over that extra unit, so using only the starting rate slightly underestimates the increase.
Try the changed production model
In section 2 of the marginal-cost lesson, try the independent question where production rises from 40 to 42 units. Keep the solution closed. Name the added quantity and units first, compare the local estimate with the exact cost increase, then explain the direction of the error.
How tutoring can help
Start with a business-calculus question or a basic concept you want to understand. Your attempt or course outline, if you have one, can help us choose examples. Before calculating, your tutor can ask you to name the requested quantity: a rate in CAD per unit, a cost change in CAD or a total cost in CAD. Compare your derivative or integral with that choice, then try the changed-model question and explain why its method fits.
Exam preparation for MATH 122
Build short mixed sets from your section’s outline: functions and limits, derivative rules, business applications and integration. Before calculating, identify whether you need a rate, a cost change or a total. Check antiderivatives by differentiating and keep algebra errors separate from interpretation errors.
Use your section’s outline to choose the chapters to review. We work through permitted practice and comparable problems, without completing graded assignments or exams on your behalf.
Independent practice
Free practice and study guides for MATH 122
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