definition of derivative f'(c)=
The derivative of a function f at a particular point c, denoted as f'(c), represents the instantaneous rate of change of f at that point
The derivative of a function f at a particular point c, denoted as f'(c), represents the instantaneous rate of change of f at that point. It describes how the function f behaves locally around c.
Formally, the derivative f'(c) can be defined as the limit of the difference quotient as the change in the input approaches zero. Mathematically, it can be expressed as:
f'(c) = lim(h->0) (f(c + h) – f(c)) / h
where h represents a small change in the input variable, c. This limit computes the slope of the tangent line to the graph of the function f at the point (c, f(c)).
The derivative f'(c) provides important information about a function. It indicates whether a function is increasing or decreasing at a given point and can help analyze the concavity of the function. Additionally, it is used to find critical points, where the derivative is zero, and to study the behavior of a function near those points.
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