Curve sketching

Examples
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Lessons
  1. Use the guidelines to sketch the graph of:

    f(x)=x3−8x3+8f(x)=\frac{x^3-8}{x^3+8}
    1. Domain
    2. Intercepts
    3. Asymptotes
    4. Compute f′(x):f' (x):
      - critical numbers
      - intervals of increase/decrease
      - local extrema
    5. Compute f′′(x):f'' (x):
      - possible inflection points
      - intervals of concavity
      - verify inflection points
  2. Use the guidelines to sketch the graph of:
    f(x)=−x3−6x2−9xf(x)=-x^3-6x^2-9x
    1. Domain
    2. Intercepts
    3. Asymptotes
    4. Compute f′(x):f' (x):
      - critical numbers
      - intervals of increase/decrease
      - local extrema
    5. Compute f′′(x):f'' (x):
      - possible inflection points
      - intervals of concavity
      - verify inflection points