## Grade 12 Calculus and Vectors

Chapter 4: Curve Sketching

A more Practical Steps for Curve Sketching

REMINDER:

- Not all steps listed below will be used in every situation. Therefore, use steps as needed.

- In some circumstances, students may be expected to use the knowledge of basic shapes of functions.

- As each step is completed, ensure the information is transcribed on to the grid/sketch.

1. Determine both x- and y-intercepts.

2. Determine vertical asymptotes and values to the left and right of the asymptotes.

3. Determine horizontal asymptotes and values above and below the asymptotes.

3. Apply first derivate test and obtain critical numbers.

4. Determine the interval of increase and decrease with the use of a table.

5. Find second derivative and verify point of concavity and points of inflection.

6. Determine oblique asymptotes and its behaviour from above and below..

**
4.1 Intervals of Increase and Decrease
4.2 First Derivative Test - Critical points, Local Maxima and Local Minima
4.3 Vertical Asymptotes and Horizontal Asymptotes
4.4 Second Derivatives - Concavity and Points of Inflection
4.5 Oblique or Slant Asymptotes
**

## Grade 12 Calculus and Vectors

Chapter 1: Introduction to* Calculus *and Vectors

Chapter 2: Derivatives

Chapter 3: Applications of Derivatives

Chapter 4: Curve Sketching

4.1 Intervals of Increase and Decrease

4.2 First Derivative Test

Critical points, Local Maxima and Local Minima

4.3 Vertical Asymptotes and Horizontal Asymptotes

4.4 Second Derivatives

Concavity and Points of Inflection

4.5 Oblique or Slant Asymptotes

Chapter 5: Derivatives of Trigonometric Functions

Chapter 6: Derivatives of Exponential Functions

Chapter 7: Introduction to * Vectors *

Chapter 8: Vector Operations and Applications

Chapter 9: Equations of Lines

Chapter 10: Equations of Planes

Chapter 11: Points, Lines and Planes

Videos for each topic contain a playlist, allowing you to choose the instructor and learning style to your liking. You can choose different videos in a topic by placing the mouse over the video and selecting a different video from the playlist. Videos of solutions to multiple example problems are also available to illustrate to students how each tools and techniques should be used.

Please refer to high school math prerequisite tree to see the recommended courses and materials one should be familiar with prior to taking up Calculus and Vectors.

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