Read the web page: What is a derivative, anyway? To answer the questions, you will need to access the PhET simulation Calculus Grapher and run it. Set the following in the simulation: shift, derivative, and grid. Zero the function.
- When you pull f(x) up, what happens to df/dx?
Set the following in the simulation: sharpness to 3rd notch, hill, derivative and grid. Zero the function. Pull f(x) upwards in the middle. What is the value (positive/zero/negative) of:
- f(x) at its maximum?
- df/dx when f(x) is at its maximum?
- df/dx to the left of f(x) at its maximum?
- df/dx to the right of f(x) at its maximum?
Set the following in the simulation: tilt, derivative, integral and grid. Zero the function.
- What happens to df/dx when f(x) is tilted downward?
- Exploration: Determine if the y-scale (grid) is the same for df/dx and f(x). Explain how you determined your answer.
Dave Buehle, Fall 2016
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