7.4.2 Points of Inflection

What is a point of inflection?

• At AS level you encountered points of inflection when discussing stationary points
  • When the sign of the first derivative (ie of the gradient) is the same on both sides of a stationary point, then the stationary point is a point of inflection

  

• A point of inflection does not have to be a stationary point however
• A point of inflection is any point at which a curve changes from being convex to being concave
  • This means that a point of inflection is a point where the second derivative changes sign (from positive to negative or vice versa)

  

• To find the points of inflection of a curve with equation y = f(x):