What applications of the second derivative do I need to know?

• The?second order derivative?(or simply?second derivative) is encountered at AS level
  • At AS level second derivatives are used to help determine the nature of a stationary point
• At A level you need to be able to use the second derivative to determine if a function is?convex?or?concave?on a given interval
  • Where a function is?convex?its graph 'curves up' and its tangent lines lie below the graph
  • Where a function is?concave?its graph 'curves down' and its tangent lines lie above the graph

• It's the sign of the second derivative (+ or -) that's important:
  • A function?f(x)?is?convex?on a given interval if and only if?f''(x)?≥?0?for every value of?x?in the interval
  • A function?f(x)?is?concave?on a given interval if and only if?f''(x)?≤?0?for every value of?x?in the interval