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