What does tell me?

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# What does tell me? - PowerPoint PPT Presentation

What does tell me?. Today students will understand the graphical significance of the derivative. Knowing if a function increases or decreases tells us something, but not everything about its possible shape.

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### What does tell me?

Today students will understand the graphical significance of the derivative.

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.

At a corner (cusp) the slopes are not the same from both sides, so the derivative does not exist.

What happens to the slope at a corner (called a cusp)?

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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.

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Assignment

HW D

See yutmrrw!

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