The discussion revolves around the geometric derivation of the derivative of the integral function f(x) = ∫(^x, _0) (dt)/(1+t^2), with the aim of showing that it equals arctan(x). Participants are exploring the relationship between the integral and its derivative, particularly focusing on the geometric interpretation and the application of the squeeze theorem.
The discussion is active, with participants providing various insights and suggestions for approaching the problem. There is a recognition of the need to clarify the problem statement, and some participants are attempting to derive the necessary relationships while others are questioning assumptions and definitions. No consensus has been reached yet, but there are productive directions being explored.
Participants note that the problem may have been misinterpreted, as the derivative of the integral is not arctan(x) but rather 1/(1+x^2). There are references to the original problem being in Swedish, which may contribute to the confusion. The discussion also highlights the importance of correctly identifying the dummy variable in the integral.
Laurentiusson said:It looks like my A is 1 and my B is 0 since the graph has a max at 1 and approaches 0 both to left and right.
Mark44 said:No. A and B aren't the max and min values of 1/(1 + t2). They are the max and min values of the integral.
I agree. We can't go further than the hints we have given without working the problem for you, which as LCKurtz says, is against the policy in this forum.LCKurtz said:After participating in and watching this thread, I don't think we can get you through this problem without working it for you, which is against forum policy. My suggestion is that it is time for you to have a face to face meeting with your teacher.
If you have a specific question about something we have written, ask it, but saying you are more and more confused doesn't give anything to go on.Laurentiusson said:I'm just more and more confused for every sentence you write. What am I actually suppoadd to do?
On the interval [x, x + h], what is the maximum value of 1/(1 + t2)? What is the minimum value of 1/(1 + t2)?Laurentiusson said:I don't have a teacher to ask which is the reason to why I'm here.
I wonder how I can see the max and mins for 1/(1+t^2). I thought I just should look for extreme points when I plot it but I guess I'm wrong.