Increasing and Decreasing Functions
March 20, 2017
Learning Goal: I will be able to identify increasing and decreasing parts of functions and use this information to connect the graphs of functions and their derivatives. Minds On: Whiteboards ­ increasing or decreasing and what it means
Action: 1. Class note + practice
2. Group task
Consolidation: Working Backwards
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Increasing and Decreasing Functions
March 20, 2017
Minds On
On your whiteboard, draw a function of your choice.
Find and label an interval of your graph that is increasing.
Find and label an interval of your graph that is decreasing.
What can you say about the tangents to the function for each of these intervals?
How does this relate to derivatives?
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Increasing and Decreasing Functions
March 20, 2017
Action
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Increasing and Decreasing Functions
March 20, 2017
Action
Without a graph
Find when the derivative is 0 (graph levels out)
Test intervals on either side of these points to find increasing and decreasing intervals. If derivative is positive, increasing, if derivative is negative, decreasing.
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Increasing and Decreasing Functions
March 20, 2017
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Increasing and Decreasing Functions
March 20, 2017
Action
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Increasing and Decreasing Functions
March 20, 2017
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Increasing and Decreasing Functions
March 20, 2017
Action
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Increasing and Decreasing Functions
March 20, 2017
Consolidation
Working Backwards
The equation of f'(x) from the previous example was f'(x) = (x + 1)(x ­ 5).
Determine the equation of the original function, f(x).
We worked backwards to figure out what the values would have been BEFORE we took the derivative. The last term can be anything, because when you take the derivative of a constant, it is 0 (it disappears).
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