Let us think about the differential function because it will
give more significant information for the function . The differential
function has two roots x=0, and x=1. So the function has two points
where the derivatives are zero. That is to say, two tangent lines at two
different point are parallel to x-axis. See the next graph of and
If x<0 , then vales of the differentiated function (green one) are
all negative. So any tangent line on (where x<0) has a negative
slope. And as x decreases from 0 the lopes of tangent lines should be decreased.
Students can compare these all facts from the above graph. There are three
changes in green graph.