2.4 Average Rate of Change of a Function

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What's an example of an instantaneous rate of change?

Speedometer on car

Can the average rate of change of an increasing function ever be negative?

The average rate of change of a function f between x=a and x=b is

f(b)-f(a)/b-a

If the average rate of change of a function between x=a and x=b is negative, then is the function necessarily decreasing on the interval (a,b)?

Is the average rate of change of a linear function the same for all intervals?

Yes

If you travel 100 miles in two hours, then your average speed for the trip is _______

100/2 = 50 mi/h

Linear functions have a ________ rate of change.

Constant

F and G have the same average rate of change between x=0 and x=1.5

The graphs of the functions f and g are shown... what interval to they have the same average rate of change?

F (red) has a greater average rate of change between x=0 and x=1

The graphs of the functions f and g are shown... which function has a greater average rate of change between x=0 and x=1

G (blue) has a greater average rate of change between x=1 and x=2

The graphs of the functions f and g are shown... which function has a greater average rate of change between x=1 and x=2

The average rate of change of a function f between x=a and x=b is slope of the line ___________ between (a, f(a)) and (b,f(b))

secant

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