What is a derivative?
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Derivatives enable us to determine how a given function is changing at a certain point on the line.
Scenario: Imagine this function represents a race car's distance from the starting line over the course of a race. What was the average speed of the car?
Scenario: Imagine this function represents a race car's distance from the starting line over the course of a race. What was the speed of the car at 2 seconds?
We'd have to evaluate the derivative of f(x) at x = 2!
Derivatives essentially enable us to see the slope of a given function at every point on the line.