(2x+1)/(8x+1)
f is increasing for x:
f is decreasing for x:
find local max/min:
y = (2x+1)/(8x+1)
y' = -6/(8x+1)^2
Since (8x+1)^2 is always positive, y' is never zero, so the are no mins or maxes.
y is always decreasing. Check its graph to see how this can be.