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Grade 12 · Calculus
Sketching Cubic Graphs (Grade 12)
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Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Determine the y-intercept of f(x) = x³ − 3x² − 9x + 5.
    (2)
    -3-2-112345-20-1010xyy = x³ − 3x² − 9x + 5(−1 ; 10) max(3 ; −22) min(1 ; −6) infl
  2. 2
    Determine the coordinates of the stationary points of f(x) = x³ − 3x² − 9x + 5.
    (2)
    -3-2-112345-20-1010xyy = x³ − 3x² − 9x + 5(−1 ; 10) max(3 ; −22) min(1 ; −6) infl
  3. 3
    State, with a reason, which stationary point is the local maximum.
    (2)
  4. 4
    Determine the coordinates of the point of inflection.
    (2)
    -3-2-112345-20-1010xyy = x³ − 3x² − 9x + 5(−1 ; 10) max(3 ; −22) min(1 ; −6) infl
  5. 5
    For which values of x is f decreasing?
    (2)
  6. 6
    For which values of x is f concave up?
    (2)
  7. 7
    Where does the point of inflection of a cubic always lie relative to the turning points?
    (2)
  8. 8
    Determine the stationary points of g(x) = x³ − 12x.
    (2)
TOTAL: 16 marks
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