The Derivative

1
The Derivative

• The derivative indicates the _____ of a function.

slope
2
The Derivative

• For an application, the derivative indicates the
  ____________________ of the function.

instantaneous rate of change
Population as a function of time ? Growth Rate
Pizza Cost as a function of size ? Change in Cost
Sales as a function of advertising ? Change in
Sales
3
The Derivative

• The derivative indicates the _____ of a function.

slope
4
AP Calculus The Derivative
The slope of a curve at a point is found by
finding the slope of the tangent line to the
curve at that point.
P
5
The Derivative
P
But how can we find the slope of a line with only
one point given?
6
The Derivative
Q
P
Select a second point near the first point
Calculate the slope through the two points.
7
The Derivative
Q
P
Move the second point closer to the first point
Calculate the slope again.
8
The Derivative
Q
P
Move the second point closer yet
Calculate the slope yet again.
9
The Derivative
Q
P
Move the second point closer again
Calculate the slope again.
10
The Derivative
Each time the second point is moved closer to the
first point, the secant line gets closer to the
_______ line.
tangent
As ?x ? 0, the slope of the secant line gets
closer to the slope of the _______ line.
tangent
11
The Derivative
12
The Derivative