Maximum and Minimum Problems
Solve optimization problems using differential calculus and explain your reasoning in English. Mathematics meets professional communication.
Learning Goals
📐 Mathematics
- Reduce a function to one variable
- Differentiate with respect to x
- Find and classify critical points
- Interpret maximum and minimum values
🌍 Language (CLIL)
- Describe mathematical steps in English
- Use correct calculus terminology
- Explain reasoning clearly and logically
- Present a solution professionally
Your Workflow
Study the Theory
Review the theory pages on maximum and minimum problems.
Solve the Examples
Work through the three guided examples using the given strategy.
Choose Your Tasks
Select 2 exercises from 1–12 and 2 from 13–20. Solve them in MathCad Prime 6.0 including an English explanation.
Upload & Present
Upload screenshots to Teams and present your solution in class.
Optimization Strategy
- Express Q as a function of one variable.
- Simplify the function as far as possible.
- Differentiate with respect to x.
- Solve f'(x) = 0 to find critical points.
- Determine whether the point is a maximum or minimum.
Use the procedures developed in previous weeks.
Presentation Requirements
- Explain what is given in the problem.
- Describe how you reduced the function to one variable.
- Show how you found the critical point.
- Explain whether it is a maximum or minimum.
- Interpret the result in context.
Focus on correct mathematical English, not perfect grammar.
Mathematical Vocabulary
Differential Calculus
- to differentiate with respect to x
- critical point
- maximum / minimum
- turning point
- gradient
- curvature / concavity
General Mathematics
- numerator / denominator
- polynomial
- power
- fraction
- intermediate step
- as far as possible
Ready to apply optimization?
Show that you can solve, explain and present mathematical reasoning in English.
Go to Exercise Pool