[MPSI/MP2I/PCSI] Continuity - solved exercise Mines-Ponts MP (fixed point and commutating functions)
Hi, today we're tackling an exercise from the MP exam at Mines-Ponts, which states that if two continuous functions f and g commute from [0,1] to [0,1], then there exists a point c such that f(c) = g(c). To do this, we must first show that f has a fixed point and then study the sequence f^n(a) as f is at every point above g.
Video outline and solution to the exercise:
00:00 - Presentation of the problem
00:31 - Hint 1 (Q1)
00:36 - Hint 2 (Q1)
00:38 - Hint 3 (Q1)
00:41 - Hint 1 (Q2)
00:45 - Hint 2 (Q2)
00:50 - Hint 3 (Q2)
00:54 - Hint 1 (Q3)
00:56 - Hint 2 (Q3)
01:03 - Hint 3 (Q3)
01:06 - Q1
02:11 - Q2
03:51 - Q3
06:01 - Conclusion on the problem
My collection of solutions to exam questions: https://fr.overleaf.com/read/fnbdzpzk...
My personal website containing lots of exercises and answer keys: https://teobernardi.wixsite.com/blog/...
Source: Mines-Ponts MP
Music: Steve Hartz - Never Get Old
#oralexams #mines-ponts #mp #mpsi #answerkey