Answer: 838860
=========================================
Plug in x = 0 to find y = f(x)
f(x) = 4^(2x+1)
f(0) = 4^(2*0+1)
f(0) = 4
The point (0,4) is on the function curve
Plug in x = 5 and compute
f(x) = 4^(2x+1)
f(5) = 4^(2*5+1)
f(5) = 4194304
The point (5, 4194304) is on the function curve
Once you have these two points, you use the slope formula to compute the average rate of change
m = (y2-y1)/(x2-x1)
m = (4194304 - 4)/(5-0)
m = 838860
The slope of the line through the two points found earlier is m = 838860, so this is the average rate of change on f(x) for the interval from x = 0 to x = 5.
