a harder example of absolute extrema of a function

Learn how to find the absolute maximum and the absolute minimum of the function f(t)=sqrt(t)/(1+t^2) on the interval [0,2]. Remember we have to get the first derivative and set it equal to 0 so we can find the critical numbers. Then we will have to check the values of the function at the critical numbers, as well as the endpoints of the interval.

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[moregirl]

You should show f'(1)<0 or any method to compare f(3^-.5) and f(2) rather than use calculator

[kobethebeefinmathworld]

Perhaps rationalize f(1/sqrt{3}) would be helpful for viewers who don't use calculators

[wuyqrbt]

Thank you dear teacher.
But if we don't have calculator how we should find it?!
I always interested about this subject:
How our former Mathematician deal with this kind of situations (I mean, without calculator)?!

[theimprudentman]

It would have been nicer if u find the f''(1/√3) and f"(2) to know which one is greater between f(1/√3) and f(2)

[MrConverse]

Aww, I was hoping for a Desmos graph at the end.