Function characteristics

# Average rate of change

The **rate of change** of a function f in an interval [x_{1},x_{2}] is: RC = f(x_{2}) – f(x_{1})

The aver**age rate of change** of a function f in an interval [x_{1},x_{2}] is

Example: f(x) = x^{2},

If f is decreasing in the interval, then ARC < 0

If f is increasing in the interval, then ARC > 0

If f is constant in the interval, then ARC = 0

**Exercise**: Calculate the ARC_{[0,3]} of these functions:

a) f(x) = x^{3} - 3

b)

Solutions: a) 9; b) 3/10

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