Maxima-minima problems

  1. Hi!

    For example y=-x^3-3x=0 gives y'=-3x^2-3 and setting y'=0 we get i and -i as the solutions. What does this say about the existence of the max and min points for the function y?

    - Kamataat
  2. jcsd
  3. Hi!

    -3x2-3=0 has no solutions in real numbers

    So, y' is always negative (as -3 is)
    Hence, y is always decreasing (no min and max)
  4. ok, thanks

    - Kamataat
  5. -x^3-3x=k

    -x^3-3x-k=0=> where b makes x only have two solutions.....
    k= -cb^4/4
    Last edited: Dec 19, 2004
  6. hi!
    how determine whether that point is the maximum or the minimum?
  7. Mark44

    Staff: Mentor

    The second derivative test is helpful. At a critical number c for which f'(c) = 0, if f''(c) > 0, (c, f(c)) is a local minimum point; if f''(c) < 0, (c, f(c)) is a local maximum point.

    There's more to this, but your calculus text should have more information about the details.

    In the future, if you have a question, start a new thread rather than adding onto an old thread. This thread is six years old.
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