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Before diving into derivatives, we must understand rates of change. A car's speedometer shows rate of change of position. A thermometer shows rate of change of temperature.
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A car travels 120 miles in 2 hours. What is its average rate of change (speed)?
The slope of a curve at any point is the instantaneous rate of change. This is the foundation of the derivative!
The Definition of a Derivative
What does f'(x) represent?