What does tell me?
Today students will understand the
graphical significance of the derivative.
''f
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Knowing if a function increases or decreases tells us something, but not everything about its possible shape.
•Draw an example of a function that is increasing everywhere. What type of function behaves like this? Is there more than one possible shape?
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Knowing if a function increases or decreases tells us something, but not everything about its possible shape.
•Draw an example of a function that is decreasing, then increasing, then decreasing again. What type of function behaves like this?
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Knowing if a function increases or decreases tells us something, but not everything about its possible shape.
•Find a function that infinitely alternates between increasing and decreasing. What type of function behaves like this?
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Sketch the slope function for each function below.
What happens to the slope at a corner (called a cusp)?
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Sketch the slope function for each function below.
What happens to the slope at a corner (called a cusp)?
At a corner (cusp) the slopes are not the same from both sides, so the derivative does not exist.
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Curve Constructor, Part One
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Curve Constructor, Part One
• What are the different orientations of arcs that can be created?
• For at least four of these, give a sketch and describe a slope statement.
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Curve Constructor, Part One
• With this tool, you can create arcs of different sizes and orientations. Then multiple arcs can be connected to make one long continuous curve. Create a few long continuous curves that use all possible orientations of arcs.
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Curve Constructor, Part One
• Using the orientations of the arcs given below, can you draw a close approximation to ANY long continuous curve?
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Closure• On what intervals is the
function increasing? Is positive or negative?
• On what intervals is the function decreasing? Is
positive or negative?
• Where is
• Sketch from this information.
'( )f x
'( )f x
'( )f x
'( ) 0?f x
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Assignment
HW D
See yu tmrrw!
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