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Application & Interpretations

Calculus

Contents: Click to skip to subtopic

5.6

  TURNING POINTS  

AI5.1

5.1: Limits, slopes of curves

pg1 A&A HL - Topic 5 - Calculus Notes.jp
AI5.2

5.2: Increasing & decreasing regions

pg2 A&A HL - Topic 5 - Calculus Notes.jp
AI5.3

5.3: Derivatives of polynomials

pg3 A&A HL - Topic 5 - Calculus Notes.jp

Problems:

  1. If f(x) = 4x², find f'(x):

  2. If g(x) = 5x³ - 2x, find g'(x):

  3. If f(x) = x⁻ ² + 7, find f'(x):

  4. If y = x + 12 - 2x, find dy/dx:

Answer
      8x      
Answer
      15x² - 2      
Answer
    -2x⁻³    
Answer
      -1     

Exercise Links: 

IXL Differentiation

Khan Academy Diff. 1

Khan Academy Diff. 2

AI5.4

5.4: Equations of tangents and normals

pg4 A&A HL - Topic 5 - Calculus Notes.jp

Exercises

2 - Tangent:Normal Revision Sheet.jpg

Solutions

Revision Sheet Answers 2.jpg
AI5.5

5.5: Introduction to integration

pg5 A&A HL - Topic 5 - Calculus Notes.jp

Problems:

  1. Find ∫2xdx:

  2. Find ∫(4t³-2)dt:

  3. Find ∫9x²dx:

Answer
      x²      
Answer
      t⁴ - 2t      
Answer
    3x³    
pg6 A&A HL - Topic 5 - Calculus Notes.jp
AI5.6

5.6: Turning Points

pg7 A&I SL - Topic 5 - Calculus Notes.jp
AI5.7

5.7: Optimisation

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AI5.8

5.8: Trapezoidal Rule 

pg9 A&I SL - Topic 5 - Calculus Notes.jp
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