Provide an example of a continuous function f:R-->R which satisfies all of the following properties
(a) non-decreasing
(b) not constant
(c) not increasing
Be sure to justify your example
I have an example as f( x ) = { 1, x<0 or x, x >= 0 with the graph that the function is constant on the left of the x axis, and increasing on the right of the x axis, but I dont know how to prove this
This is not obvius.
Consider the function:
if , and if
Now there exist points such that ,
but the function is still not increasing in no matter what points you pick.
Weierstrass function - Wikipedia, the free encyclopedia is a continuous function with the same attribute. There is no interval where the function is increasing or decreasing.
The only one that mentioned "interval" that I'm aware of was Defunkt trying to explain my answer to the OP according to what he wrote. And in your example .
Perhaps the OP meant that there is no INTERVAL where the function increases or decreases and then yours or Wierstrass' function work fine.
It never minds though, since the OP knows better because "his professor told him".
Tonio