5.7 The graphs of f, f' and f", second derivative

Key ideas

• The derivative may be represented physically as a rate of change and geometrically as the gradient or slope function.

• I can explain the relationship between a function, its derivative and the second derivative in terms of maxima, minima, points of inflexion and roots.

• I can discuss graphical behaviour of functions, including the relationship between the graphs of f, f' and f" 

• I can sketch functions and derivatives when given a derivative, a second derivative or function as a graph