Applications of Calculus

Curriculum details

Strand

Calculus (Strand 3)

Sub-strand

Applications of Calculus (3.2)

Content standard

2.3.2.CS.1 - Find maximum and minimum values and points of a function, sketch the functions, and Solve some real life problems. 2.3.2.LO.1 Investigate the turning point of a function.

Indicator

2.3.2.LI.2 - Use the second derivative of a function to classify the maximum, minimum and saddle point of that function and perform curve sketching.

Suggested placement

Semester 2, Week 14 (Week 34 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

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Curriculum reference

NaCCA curriculum document, p. 408

Exemplars (from the NaCCA curriculum)

Talk for Learning, Think-pair-share, Experiential Learning and Group Work/Collaborative Learning.
Activity 1: Turning points Learners are to work in pairs or small groups to discuss how to classify turning points.

From the first derivative test, if f' moves from positive to negative about a point, then that point is local maximum. Likewise, if f' moves from negative to positive about a point, then that point is local minimum.
Theorem (Second derivative Test) Given a continuous function 𝑓 if 𝑓 -- (𝑥)| 04; > 0 then the point (𝑐, 𝑓(𝑐) is a minimum and if 𝑓 -- (𝑥) < 0 the point (𝑐, 𝑓(𝑐) is maximum if 𝑓 -- (𝑥) = 0 then (𝑐, 𝑓(𝑐) a saddle point
Example: Classify the turning point(s) of the following 𝑦 = 𝑥 " − 9𝑥 ) + 24𝑥 , ) 𝑦 = 𝑥 − 9𝑥
Teaching and Learning Resources:
- Cardboards
- Reading resource
- Colour pens
- Notebook
- Graph sheets
- Mathematical sets
- Technological tools
Assessment (2.3.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.