What was your life's turning point?

Maximum or Minimum Turning Point?

• Just looking for a theory on how to work out a max or min turning point? For example if the turning point was (4,0)? Thanks!

• Answer:

  Take the first derivative ( This gives the slope) Equate the first derivative to zero (zero slope = turning point). This should give a value for x ( and hence y) Take the second derivative and replace x with the value obtained above(if there are still x terms). If it is zero, it is a point of inflection (neither max nor min) If it is negative, it is a maximum If it is positive, its a minimum eg y = x^2 dy/dx = 2x = 0 gives x - 0 and so y = 0 d2y/dx2 = 2 which is positive. So y = x^2 has a minimum at (0, 0)