IB DP Maths: AA HL复习笔记5.2.6 Derivatives & Graphs

How are derivatives and graphs connected?

• • asymptotes – vertical and horizontal
  • intervals where the graph is increasing and decreasing
  • intervals where the graph is concave down and concave up
• Not all graphs have all of these properties and not all can be determined without knowing the expression of the function
• However questions will provide enough information to sketch
  • the shape of the graph
  • some of the key properties such as roots or turning points

How do I sketch the graph of y = f'(x) from the graph of y = f(x)?

How do I sketch the graph of y = f''(x) from the graph of y = f(x)?

Is it possible to sketch the graph of y = f(x) from the graph of a derivative?

• Worked Example