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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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www.brainybetty.com something, but not everything about its possible shape.

www.brainybetty.com something, but not everything about its possible shape.

Sketch the slope function for each function below. something, but not everything about its possible shape.

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

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Sketch the slope function for each function below. something, but not everything about its possible shape.

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 something, but not everything about its possible shape.

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Curve Constructor, Part One something, but not everything about its possible shape.

• 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 something, but not everything about its possible shape.

• 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 something, but not everything about its possible shape.

• Using the orientations of the arcs given below, can you draw a close approximation to ANY long continuous curve?

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Closure something, but not everything about its possible shape.

• 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 something, but not everything about its possible shape.

HW D

See yutmrrw!

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