§2.7. Derivatives.

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Presentation transcript:

§2.7. Derivatives

Tangents

Velocities

Rates of change Problem: Suppose y is a function of x and y = f(x). Find the instantaneous rate of change of y with respect to x. Solution: If x changes from x1 to x2, then the change in x is called the increment of x and denoted by x = x2 – x1 and the corresponding change in y is called the increment of y and is given by y = f(x2) – f(x1). The average rate of change of y with respect to x over the interval [x1, x2] is given by y/x = [f(x2) – f(x1)]/(x2 – x1)

Derivatives