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Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Calculus



  • Students will use the second derivative test to find and verify maxima and minima in word problems.
  • Students will solve optimization in functions and further explore, as time and teacher permit, using parametric functions as well.
  • Students will try to make a connection with how to understand these topics in IB Mathematics courses and on their final assessments.


  • Maximize
  • Minimize
  • Constraint
  • Critical Points

About the lesson

In this activity, students will learn how to use the second derivative test to find maxima and minima in word problems and solve optimization in parametric functions. Students will be finding a function’s critical points by hand and through the handheld. Although there is no calculator file to download to the handheld, the key to this activity is for students to create accurate diagrams for each problem. The handheld will be used to aid the student, but much of the work can be done without a handheld.

Students will use the file Optimization.tns to help guide them through the activity.

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