2. Curve Sketching
  3. Curve Sketching and the First Derivative

Answers


      • \( f(x) \) is increasing on \( (-\infty, -2) \) and \( (-1, 0) \)
      • \( f(x) \) is decreasing \( (-2, -1) \) and \( (0, \infty) \)
      • \( f(x) \) is decreasing on \( (-\infty, 1) \)
      • \( f(x) \) is decreasing \( (1, \infty) \)
      • \( f(x) \) is increasing on \( (-\infty, -1) \) and \( (-1, \infty) \)
      • \( f(x) \) is increasing on \( (-\infty, -\frac{1}{2}) \)
      • \( f(x) \) is decreasing \( (-\frac{1}{2}, \infty) \)
    1. \( x = \frac{2}{3} \)
    2. \( x = -3, 1 \)
    3. \( x = -3, \frac{1}{3} \)
    4. \( x = \frac{1}{3} \)
  3. Increasing on \( (-\infty, -2), (3, \infty) \); decreasing on \( (-2, 3) \)
  4. \( (5,7) \)
  5. Increasing on \( (-\infty, -1), (1, \infty) \); decreasing on \( (-1, 1) \).
    Graph of cubic with characteristics described in answer
  6. Increasing on \( (-\infty, -7), (-7, \infty) \); does not decrease
  7. Decreasing on \( (-\infty, -\sqrt{5}), (0, \sqrt{5}) \)
    1. \( A = -2 \)
    2. \( A = 9 \)
  9. Increasing on \( (-5, 1), (3, \infty) \)
  10. Increasing on \( (-3, 0), (3, \infty) \); decreasing on \( (-\infty, -3), (0, 3) \)
  11. Answers may vary. One possible graph is
    Quartic opening up with turning points at (-2, 1), (3, 2), zero at x=-3, 1/2
  12. \( g(x) = 2x^3 - 3x^2 - 12x + 6 \)