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Chapter 4 · Grade 12 Advanced
Applications of Differentiation
Now that we can differentiate, we use derivatives to solve real problems — approximating, optimising, sketching, and modelling change in the physical and economic world.
Lessons
Lesson 1 · G12 4.1
Linear Approximation and Newtons Method
Using tangent lines to approximate.
Open lesson → Lesson 2 · G12 4.2Indeterminate Forms and LHopitals Rule
Limits of 0/0 and infinity/infinity.
Open lesson → Lesson 3 · G12 4.3Maximum and Minimum Values
Critical points and extrema.
Open lesson → Lesson 4 · G12 4.4Increasing and Decreasing Functions
First-derivative test.
Open lesson → Lesson 5 · G12 4.5Concavity and the Second Derivative Test
Curvature and inflection points.
Open lesson → Lesson 6 · G12 4.6Overview of Curve Sketching
Putting it all together.
Open lesson → Lesson 7 · G12 4.7Optimization
Maximising area, volume, profit.
Open lesson → Lesson 8 · G12 4.8Related Rates
When several quantities change together.
Open lesson → Lesson 9 · G12 4.9Rates of Change in Economics and the Sciences
Marginal cost, velocity, growth.
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