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Term 7 · Year 2

Term 7 — Applications of the Derivative

Optimization, related rates, curve sketching, introductory Taylor.

10 lessons  ·  10 published ·  ~32h of study

(Year 2 — Differential Calculus and Probability)

Classes (didactic grouping)

Each Class groups 2–5 Lessons by topic. Click on a Lesson to study the content.

Class A — Maxima, minima and optimization

~9h · 3 lessons
  1. Lesson 61
    Maxima and Minima
    Critical points, 1st and 2nd derivative tests
    published →
  2. Lesson 62
    Applied Optimization
    Optimal box, minimum cost, applications
    published →
  3. Lesson 63
    Curve Sketching
    Increase/decrease intervals, concavity, inflection
    published →

Class B — L'Hôpital and Taylor

~9h · 3 lessons
  1. Lesson 64
    L'Hôpital's Rule
    0/0, ∞/∞ indeterminate forms
    published →
  2. Lesson 65
    Taylor Polynomials
    Pₙ(x) = Σ f^(k)(a)(x-a)ᵏ/k!, applications
    published →
  3. Lesson 66
    Concavity and Inflection Points
    f'', inflection points, sketching graphs
    published →

Class C — Marginal analysis and kinematics

~6h · 2 lessons
  1. Lesson 67
    Marginal Analysis in Economics
    Marginal cost, elasticity, applications
    published →
  2. Lesson 68
    Kinematics: Position, Velocity, and Acceleration
    v(t), a(t), motion problems
    published →

Class D — Newton-Raphson + synthesis

~6h · 2 lessons
  1. Lesson 69
    Newton-Raphson Method
    Iterative method for f(x) = 0
    published →
  2. Lesson 70
    Consolidation Term 7: Maxima, L'Hôpital, Taylor, Newton
    Synthesis: 50 mixed derivative-application problems
    published →

Test yourself this term

There are 10 exam versions covering this term, each with answer key + step-by-step solutions. Take one after each group of lessons.

Open exams for Term 7 →