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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.

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what does tell me

What does tell me?

Today students will understand the graphical significance of the derivative.

slide2
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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slide3
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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slide4
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
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 below1
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
Curve Constructor, Part One

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curve constructor part one1
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 one2
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 one3
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
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
Assignment

HW D

See yutmrrw!

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