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Overview
Grade 12 Math
Financial Mathematics
3. Analyze an investment portfolio in terms of interest rate, rate of return, and total return
3.3 Marginal cost, and minimizing cost & average cost
Marginal Cost and Minimizing Average Cost
Marginal cost is the cost of one more unit; average cost is total cost per unit.
What You'll Learn
Marginal cost is the cost of one more unit: the derivative of total cost.
Average cost is total cost divided by the number of units.
Average cost falls when marginal cost is below it and rises when marginal cost is above it.
So marginal cost crosses average cost exactly at the minimum of average cost.
To minimize average cost, set its derivative to zero; the solution satisfies MC equals AC.
What You'll Practice
1
Finding marginal cost from polynomial and rational cost functions
2
Setting marginal cost equal to zero and solving for optimal quantity
3
Computing average cost and marginal average cost using derivatives
4
Using the quadratic formula to find cost-minimizing quantities
5
Comparing multiple solutions to determine which minimizes cost
Why This Matters
Understanding marginal and average cost is essential for business optimization and economic decision-making. These concepts help you determine the most efficient production levels, minimize expenses, and maximize profitskills directly applicable to economics, business management, and real-world entrepreneurship.
Before You Start — Make Sure You Can:
This Unit Includes
10 Video lessons
Learning resources
Skills
Marginal Cost
Average Cost
Derivatives
Cost Minimization
Optimization
Quadratic Formula
Product Rule
Economic Applications
NS Curriculum Aligned