Limit Definition of Derivative
limit (as h approaches 0)= F(x+h)-F(x)/h
The limit definition of derivative is a mathematical formula used to find the slope of the tangent line to a curve at a specific point. It involves taking the limit as the difference between two points on the curve approaches zero.
If we let f(x) be a function defined on an interval, and choose a point a within that interval, we can define the derivative of f(x) at a as:
f'(a) = lim (h → 0) [f(a+h) – f(a)]/h
In this formula, h represents the difference between the point a and a point slightly to the right of a. As h approaches zero, the formula calculates the slope of the tangent line to the curve at the point a. This slope is therefore known as the derivative of the function at that point.
The limit definition of derivative can be used to find the instantaneous rate of change of a function at any given point. By calculating the derivative at multiple points, we can also determine whether the function is increasing or decreasing at those points, and whether it has maximum or minimum values.
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