Exploring Monotonous Functions: Understanding the Unique Solution

[trambolin]

Almost correct. Be careful, something happens at around 0.5, if you can plot it via some software or even with some calculator you will see it.

 

[Physicsissuef]

yes,
x=-2, y=0.0534
x=-1, y=0.259
x=0,5, y=4.88

x=1 , y=0

so it is monotonic increasing for $(-\infty,1)$
And how will I know from which point to which one is monotonic increasing, and decreasing? Should I look first for the 0?

 

[trambolin]

First of all, you cannot write $(-\infty,1)$, I understand that you are trying to say somewhere before 1. But what you write is all points from negative infinity to 1 excluding only 1. These are very dangerous mistakes, that you cannot do even when you are asleep!

Regarding your question, just check your notes for finding maxima and minima of functions. I think that is a fair hint for it.

 

[Physicsissuef]

First of all, you cannot write $(-\infty,1)$, I understand that you are trying to say somewhere before 1. But what you write is all points from negative infinity to 1 excluding only 1. These are very dangerous mistakes, that you cannot do even when you are asleep!

Regarding your question, just check your notes for finding maxima and minima of functions. I think that is a fair hint for it.

on this fuction minima is x=1, but maxima I don't know... Why $(-\infty,1)$ (moonotonic decreasing) is not correct?