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Introduction to Derivatives


Preview of Introduction to Derivatives

The Concept of the Derivative

Differentiable  -  A function f is said to be differentiable at a point x = a if f'(a) exists.
Difference Quotient  -  The difference quotient,


represents the slope of an arbitrary secant line connecting the point (x, f (x)) and the nearby point (x + h, f (x + h)) on the graph of f .
Derivative  -  The derivative of f is denoted as f'(x) , and it is the function that gives the slope of the graph of f at the point (x, f (x)) . Written as the limit of the difference quotient, the derivative of f (x) is


Secant  -  The secant line is a line connecting two points on the same curve
Tangent  -  The tangent to a curve is the line that just touches the curve at one point. At the point where the tangent meets the curve, they have the same slope.