Workout: What is a derivative anyway?

Read

Read the web page: What is a derivative, anyway?

Launch

Run the PhET simulation, Calculus Grapher.

Set up

Check the following in the simulation: select the hill (shown in yellow), move the sharpness tool to the 3rd notch, and check derivative and grid. Zero the function. Your screen should look like the image on the right.

Answer these questions

When you drag f(x) up, what happens to df/dx?

Now 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?

Now 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

Article 280
Last Modified: August 11, 2018