SLIDE 1
Geometric Interpretation of the Derivative (Review) Geometric - - PowerPoint PPT Presentation
Geometric Interpretation of the Derivative (Review) Geometric - - PowerPoint PPT Presentation
Geometric Interpretation of the Derivative (Review) Geometric Interpretation of the Derivative (Review) The derivative of a function f ( x ) at point x 0 is the slope of the tangent line at that point. Geometric Interpretation of the Derivative
SLIDE 2
SLIDE 3
Geometric Interpretation of the Derivative (Review)
The derivative of a function f (x) at point x0 is the slope of the tangent line at that point.
SLIDE 4
Geometric Interpretation of the Derivative (Review)
The derivative of a function f (x) at point x0 is the slope of the tangent line at that point.
SLIDE 5
Geometric Interpretation of the Derivative (Review)
The derivative of a function f (x) at point x0 is the slope of the tangent line at that point.
SLIDE 6
Geometric Interpretation of the Derivative (Review)
The derivative of a function f (x) at point x0 is the slope of the tangent line at that point.
SLIDE 7
Physical Interpretation of the Derivative
Movement at constant veloctity
SLIDE 8
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 9
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 10
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 11
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 12
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 13
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 14
Physical Interpretation of the Derivative
Movement at constant veloctity
Consider a train travelling at constant velocity, say, 80km per hour.
SLIDE 15
Physical Interpretation of the Derivative
Movement at constant veloctity
SLIDE 16
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points:
SLIDE 17
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points:
SLIDE 18
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points:
SLIDE 19
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points: The slope of this line would be:
SLIDE 20
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points: The slope of this line would be: m = ∆y ∆x
SLIDE 21
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points: The slope of this line would be: m = ∆y ∆x = ∆s ∆t
SLIDE 22
Physical Interpretation of the Derivative
Movement at constant veloctity
We can plot these points: The slope of this line would be: m = ∆y ∆x = ∆s ∆t That’s average velocity!
SLIDE 23
SLIDE 24
Let’s say that the distance traveled by a car is represented in this graph:
SLIDE 25
Let’s say that the distance traveled by a car is represented in this graph:
SLIDE 26
Let’s say that the distance traveled by a car is represented in this graph:
SLIDE 27
Let’s say that the distance traveled by a car is represented in this graph:
SLIDE 28
Let’s say that the distance traveled by a car is represented in this graph:
SLIDE 29
Let’s say that the distance traveled by a car is represented in this graph:
SLIDE 30
Let’s say that the distance traveled by a car is represented in this graph: speed = lim
∆x→0
∆y ∆x
SLIDE 31
Let’s say that the distance traveled by a car is represented in this graph: speed = lim
∆x→0
∆y ∆x : instantaneous rate of change!
SLIDE 32