how to find max,min points of a cubic graphs?

• Bigcable22

  30 May 08, 10:37

  how to find max,min points of a cubic graphs? without the use of gc is there any formula to deduce max point and min point, as well as vertex(turning point)?

• the Bear

  30 May 08, 10:42

  use calculus..

  where the change in y over the change in x = zero is the turning point... in other words, dy/dx = 0

  uhh.. there is no minimum or maximum point in cubic graphs...

• ^tamago^

  30 May 08, 11:06

  obtain deriative of the function (dy/dx), then find the value(s) of x when dy/dx = 0.
  
  turning points can be a maximum (d²y/dx² < 0 when dy/dx = 0), a minimum (d²y/dx² > 0) or a point of inflexion (d²y/dx² = 0).
  
  for polynomials of degree 3 (ax³+bx²+cx+d or cubic equation), you should have either:
  for b² > 3ac, 2 turning points (1 max, 1 min)
  for b² = 3ac, a single point of inflexion
  for b² < 3ac, no turning points (dy/dx = 0 will have no real solutions).