The Derivative as a Function

1
The Derivative as a Function
We considered the derivative a function f at a
number a
Now let the number a vary. Replace a with x and
we obtain
2
The Derivative as a Function
3
The Derivative as a Function
4
The Derivative as a Function
Note using the traditional notation y f (x) the
independent variable is x and the dependent
variable is y.
We have a number of other notations to define the
derivative.
5
The Derivative as a Function
Conditions when a function is not differentiable
at a
A corner
A discontinuity
A vertical tangent
6
The Derivative as a Function
7
The Derivative as a Function
Estimate the slope at several points and graph
the derivative
8
The Derivative as a Function