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How steep is a curve? Rate of change
Play Rate of Change
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How to play Rate of Change
- Read the first step: a curve has a different steepness at each point.
- Move the sliders and switches to change the diagram and watch what happens. The readout under the picture shows the numbers.
- Answer each question. If you are wrong you get a hint and can try again, with no penalty.
- Some steps ask you to make something happen, such as hitting a target value. Experiment until it works.
- Finish the lesson to earn XP and see how many questions you got right first time.
Tips and strategy
- Do not rush. The controls are there to be played with, so try extreme values as well as sensible ones.
- Say what you notice out loud or write it down before you press Continue.
- Use the hint when you are stuck, and then try to explain the answer in your own words.
- Look at how tilted the tangent line is, not at the curve itself.
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FAQ
Rate of Change: questions
What is a derivative?
The slope of a curve at a single point: how fast the output is changing compared with the input there.
What is a tangent line?
A straight line that touches a curve at one point and has the same steepness as the curve there.
Why is the slope 0 at the bottom of a curve?
At the lowest point the curve stops falling and has not yet started to rise, so it is momentarily flat.
What age is this lesson for?
It suits ages 14 and up as a first look at calculus. Younger learners who know slope can try it too.
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