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):
- Remember – the first derivative (ie the gradient) does NOT have to be zero at a point of inflection!