Loading in 5 sec....

The Difference Quotient PowerPoint Presentation

The Difference Quotient

- By
**bin** - Follow User

- 108 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' The Difference Quotient ' - bin

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

The Difference Quotient

Thursday, Jan 30th

Goal: to develop a general equation for rate of change

rise

Slope =

rise

run

run

Goal: to develop a general equation for rate of change (aka. slope of a secant)

x

rise

Slope =

rise

run

run

Goal: to develop a general equation for rate of change (aka. slope of a secant)

=

f(b) – f(a)

b – a

a

b

x

Slope =

rise

rise

run

run

=

Goal: to develop a general equation for rate of change (aka. slope of a secant)

f(b) – f(a)

b – a

Notice: b = a + h

h

a

b

x

Slope =

rise

run

rise

=

f(b) – f(a)

b – a

run

Goal: to develop a general equation for rate of change (aka. slope of a secant)

Slope =

Notice: b = a + h

f(a + h) – f(a)

a + h – a

h

a

b

x

Slope =

rise

run

rise

=

f(b) – f(a)

b – a

run

Goal: to develop a general equation for rate of change (aka. slope of a secant)

Slope =

Notice: b = a + h

f(a + h) – f(a)

a + h – a

=

h

f(a + h) – f(a)

h

a

b

x

f(a + h) – f(a)

h

Slope =

rise

run

How could we use this equation for the slope of a secant to determine the slope of a tangent?

Let h 0

h

a

b

x

f(a + h) – f(a)

h

Slope =

How could we use this equation for the slope of a secant to determine the slope of a tangent?

Let h 0

h

a

b

x

Miss Timan – in a fit of marking madness – threw the Advanced Functions off her balcony (not a true story). The height of the exams above the ground (in metres) can be modelled by: f(t) = 15 – 4.9t2.

Develop an expression for the instantaneous rate of change (velocity) of the falling exams.

Miss Timan – in a fit of marking madness – threw the Advanced Functions off her balcony (not a true story). The height of the exams above the ground (in metres) can be modelled by: f(t) = 15 – 4.9t2.

Develop an expression for the instantaneous rate of change (velocity) of the falling exams.

f(a + h) – f(a)

h

Slope =

f(a) = 15 – 4.9a2

f(a + h) = 15 – 4.9(a + h)2

Miss Timan – in a fit of marking madness – threw the Advanced Functions off her balcony (not a true story). The height of the exams above the ground (in metres) can be modelled by: f(t) = 15 – 4.9t2.

We just discovered that v(t) = – 9.8t.

What is the acceleration of the exams (aka. the rate of change of velocity)?

Miss Timan – in a fit of marking madness – threw the Advanced Functions off her balcony (not a true story). The velocity of the exams above the ground (in metres) can be modelled by: v(t) = – 9.8t

Develop an expression for the instantaneous rate of change of the velocity of the falling exams.

v(a + h) – v(a)

h

Slope =

v(a) = – 9.8a

v(a + h) = – 9.8(a + h)

Homework

Download Presentation

Connecting to Server..