Exploring Derivatives
Instructions:
- Active the box Trace derivative to sketch the derivative.
- Slowly drag the point to observe how the slope of the tangent segment changes. (If you can't see the drag button, click on "controls")
- Observe what happens to when is increasing and decreasing.
- Change the function . Repeat the previous step. Examples:
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- After trying out some functions, answer the questions at the bottom.
Using the graph of , what can you say about ?
Using the graph of , what can you say about ?
Using the graph of , what can you say about ?
After trying different functions, what do you notice about ? In other words, when is positive and when is negative?
Can you come up with a function where the derivative is negative at all x values?