Section 5.5: Making Connections and Rates of Change (p. 290 - 295)
Key Concepts:
Prior Knowledge:
Rates of Change and Slope of a Curve
Rates of Change and Slope of a Curve
Numerical Calculations for Rates of Change
Note: Calculations in the last table show instantaneous rates of change from both sides of the tangent or point of interest. Take the average of the two and the instantaneous rate of change at (2, 16) is 10. When given an equation, substitute approaching values of x "below" (e.g. 1.999) and "above" (e.g. 2.001) the x-value of interest, then take the average of the two "slopes" for the instantaneous rate of change at a particular x-value.
Note: Calculations in the last table show instantaneous rates of change from both sides of the tangent or point of interest. Take the average of the two and the instantaneous rate of change at (2, 16) is 10. When given an equation, substitute approaching values of x "below" (e.g. 1.999) and "above" (e.g. 2.001) the x-value of interest, then take the average of the two "slopes" for the instantaneous rate of change at a particular x-value.
Lessons for Section 5.5:
1. Making Connections with Sinusoidal Functions
Note: As per our discussion regarding instantaneous rates of change, we will calculate two instantaneous rates of change (one from the left of the tangent, and one from the right of the tangent) then use the average of the two rates as our answer.
Check out Video #2 from Prior Knowledge.
Note: As per our discussion regarding instantaneous rates of change, we will calculate two instantaneous rates of change (one from the left of the tangent, and one from the right of the tangent) then use the average of the two rates as our answer.
Check out Video #2 from Prior Knowledge.
2. Applications of Sinusoidal Functions
- Ferris Wheel
- Ferris Wheel
- Simple Harmonic Motion of a Spring
Assigned Practices:
- Worksheet 5-5
- eBook: Do exercises on p. 297 #1 to 4, #6 to 7, #10 to 12
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SmartBoard Notes:
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