The difference quotient measures the average rate at which a quantity changes over an interval by taking the difference between two points on a graph and dividing it by their corresponding x-values.
Imagine you have two points on your favorite roller coaster track. The difference quotient would be like calculating the average speed between those two points by dividing the vertical distance traveled by the horizontal distance covered.
Limit Definition of Derivative: A formula that uses difference quotients to find derivatives.
Tangent Line Approximation: An estimation technique that uses difference quotients to approximate the slope of a curve at a specific point.
Instantaneous Rate of Change: The rate at which a quantity is changing at a specific moment in time.
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