What does a derivative actually mean?

It tells you how fast something is changing at a particular moment. On a graph, it’s the slope of the curve at that point.

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Can you give me an everyday example?

Think of a car journey. Average speed describes the whole trip. A derivative is like reading the speedometer at one instant.

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Quiz me on what I just learned.

A curve rises, reaches a smooth peak, then falls. What is its derivative exactly at the peak, and why?

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