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Grade 12 Calculus and Vectors
Chapter 4: Curve Sketching

A more Practical Steps for Curve Sketching

- 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

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