2.4 Average Rate of Change of a Function

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?

No

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)?

No

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