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What does tell me?

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?

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  1. What does tell me? Today students will understand the graphical significance of the derivative.

  2. 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? www.brainybetty.com

  3. 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? www.brainybetty.com

  4. 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? www.brainybetty.com

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  7. Sketch the slope function for each function below. What happens to the slope at a corner (called a cusp)? www.brainybetty.com

  8. 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)? www.brainybetty.com

  9. Curve Constructor, Part One www.brainybetty.com

  10. 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. www.brainybetty.com

  11. 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. www.brainybetty.com

  12. Curve Constructor, Part One • Using the orientations of the arcs given below, can you draw a close approximation to ANY long continuous curve? www.brainybetty.com

  13. 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. www.brainybetty.com

  14. Assignment HW D See yutmrrw! www.brainybetty.com

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