instantaneous rate of change
Download
Skip this Video
Download Presentation
Instantaneous Rate of Change

Loading in 2 Seconds...

play fullscreen
1 / 50

Instantaneous Rate of Change - PowerPoint PPT Presentation


  • 189 Views
  • Uploaded on

Instantaneous Rate of Change. Sections 3.1-3.3 Section 4.1. Average Change. Defined equations in terms of their changes e.g., exponential  constant percentage change Will use this concept motivate derivatives. Average Change. Rate of change Difference between two values

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Instantaneous Rate of Change' - winka


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
instantaneous rate of change

Instantaneous Rate of Change

Sections 3.1-3.3

Section 4.1

average change
Average Change
  • Defined equations in terms of their changes
    • e.g., exponential  constant percentage change
  • Will use this concept motivate derivatives
average change3
Average Change
  • Rate of change
    • Difference between two values
  • Percentage change
    • Difference between two values as a percentage of the original value
  • Average change
    • Change per unit of time
average change4
Average Change
  • Ex: r(t) = pool sales
average change6
Average Change
  • Rate of change
  • Percent change
  • Average change
average change7
Average Change

Rate of change from April to August

Rate of change

average change8
Average Change

Rate of change from April to August

r(8) - r(4)

average change9
Average Change

Average rate of change from April to August

r(8) - r(4)

average change10
Average Change

Average rate of change from April to August

r(8) - r(4)

8-4

average change11
Average Change

Average rate of change from April to August

r(8) - r(4)

8-4

average change12
Average Change
  • In-Class
    • Pg 167: 1, 2, 4, 6, 7, 8, 10
average change13
Average Change

Average rate of change from April to August

r(8) - r(4)

8-4

average change14
Average Change

Average rate of change from April to August

rise

run

average change15
Average Change

Average change between two points

Slope of the secant line between the two points

=

instantaneous rate of change16
Instantaneous Rate of Change
  • Rate of change at this instant
    • Average rate of change over an infinitesimally small range
instantaneous rates of change
Instantaneous Rates of Change
  • Tangent line
    • Secant line that touches the graph at the point evaluated

The instantaneous rate of change is the slope of the tangent line at the point evaluated

instantaneous rates of change23
Instantaneous Rates of Change
  • Local linearity
    • Zoom in enough and anything looks like a line.
instantaneous rates of change27
Instantaneous Rates of Change
  • Tangent lines don’t intersect graph at the point of tangency, but
  • Tangent lines can intersect graph at other points
instantaneous rates of change33
Instantaneous Rates of Change
  • Exists only where you have a continuous function
  • Does not exist at breakpoints
instantaneous rates of change38
Instantaneous Rates of Change
  • In-Class
    • Pg 185: 7, 8, 9, 10
derivatives

Derivatives

Section 3.3

Section 4.1

derivatives45
Derivatives
  • Another phrase for instantaneous rate of change

Instantaneous rate of change

Rate of change

=

=

Slope of curve

Slope of tangent line

=

=

Derivative

derivatives46
Derivatives
  • Notation

“Derivative of f with respect to x”

derivatives47
Derivatives
  • Ex: Profit versus number of employees
  • p(t) = 20*ln(t)
derivatives49
Derivatives
  • Notation
  • Interpretation
derivatives50
Derivatives
  • In-Class
    • Pg 203: 1, 2, 4, 6, 10
ad