instantaneous rate of change (2.1)
slope of the tangent line
The instantaneous rate of change, also known as the derivative, is the rate at which a function is changing at a specific moment or point. It represents the slope of the tangent line to the graph of the function at that point. The derivative can be found using calculus by taking the limit of the average rate of change as the interval becomes infinitely small. The derivative of a function f(x) is denoted by f'(x) or dy/dx, where y is the dependent variable and x is the independent variable. The instantaneous rate of change is essential in many fields of study, including physics, economics, and engineering, where it helps in understanding how fast quantities are changing at specific moments or points.
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