0 0 votes True / false ? In continuous function if we have three stationary points then always it will be case that either one is maxima and two are minima or one is minima and two are maxima ? I think it is true but i am concerned about constant fucntion Calculus calculus engineering-mathematics maxima-minima + – rahul sharma 5 2.4k views answer comment Share Follow Print See all 5 Comments 5 5 Comments reply Show 2 previous comments Rupendra Choudhary commented Jul 2, 2017 reply Follow flag yes, it is. 0 0 replyShare rahul sharma 5 commented Jul 2, 2017 reply Follow flag Can you once check nitish comments below for inflection point? 0 0 replyShare Rupendra Choudhary commented Jul 2, 2017 reply Follow flag Hello rahul , i'm sorry for ignoring that point. yes! he is right. actually maxima/ minima(local or global) means first derivative=0 but first derivative=0 doesn't mean it's minima maxima point , as it may be inflection which is neither maxima or minima. like in y=x3 , x=0 is stationary point where first derivative is =0 but that point is neither maxima or minima. so in that way your claim is wrong. sorry from my side for wrong answer. 0 0 replyShare Please log in or register to add a comment.
0 0 votes no, it is not always true..what if graph has a structure like 'W'....it will have one maxima and two minima joshi_nitish answered Jun 30, 2017 joshi_nitish comment Share Follow See all 8 Comments 8 8 Comments reply rahul sharma 5 commented Jul 1, 2017 reply Follow flag But its a form of sin wave W,here every 3 critical points means 2 maxima and 1 minima or vice versa 0 0 replyShare Akriti sood commented Jul 1, 2017 reply Follow flag @rahul.how sin wave has 2 minima and 1 maxima?can u explain?? 0 0 replyShare joshi_nitish commented Jul 1, 2017 reply Follow flag sin wave take maximum and minimum at infinite points...sin is a periodic function...for a periodic function if maxima or minima exist, there are infinite points where it can be taken 0 0 replyShare Akriti sood commented Jul 1, 2017 reply Follow flag yes nitish.thats what i am saying .and sin has -1 as minima ans +1 as maxima 0 0 replyShare rahul sharma 5 commented Jul 1, 2017 reply Follow flag @Nitish :- what if graph has a structure like 'W'....it will have one maxima and two minima If it has one maxima and two minima then it satisfies the statemet? 0 0 replyShare joshi_nitish commented Jul 1, 2017 reply Follow flag sorry, i had seen only latter part of qsn where you have written one minima and two maxima. 0 0 replyShare rahul sharma 5 commented Jul 1, 2017 reply Follow flag So is this statement always true ? Will it hold for stationary points or only for critical points?My thought that it will be true for every three stationary points and as critical points are also stationary points so holds for them also.Please correct if i missed anything 0 0 replyShare joshi_nitish commented Jul 1, 2017 reply Follow flag It will follow...but one issue, if it is a point of inflexion...where second derivative is zero...inflexion point is stationary because first derivative is zero but it will neither be Maxima nor minima because second derivative is zero 0 0 replyShare Please log in or register to add a comment.
