The Second Derivative
We can decide whether a function is increasing
or decreasing by looking at the sign of its derivative. To decide
whether f ' is increasing or decreasing, we must look at
the sign of its derivative (the derivative of f '). This
derivative of f ' (i.e. the derivative of the derivative
of f) is called the second derivative
of f and is denoted by f ''.
Example
If
f(x) = 3x^{3} + 11x^{2}
+ x + 1
then
f '(x) = 9x^{2} + 22x
+ 1
and
f ''(x) = 18x + 22.
Exercise
