Let 
be a function
which is twice differentiable, with 
its
first derivative and 
its second derivative function. The knowledge about 
and 
gives us information
about it 
:
(i) 
for 
implies
that is strictly concave
upward in 
.
(ii) 
for implies
that is strictly concave
downward in .
(iii) 
may imply
that has a point of
inflection at 
.
Keeping these properties and that of ,
try the examples with quizzes in them.
Instruction for using the applet
- Select a function from the combo box and click on Sample Example or enter in the input box, if familiar with the syntax, given in the bottom and click New Function
- Drag the slider to check the derivative for different values of x.