0 votes 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 asked Jun 30, 2017 rahul sharma 5 926 views answer comment Share Follow See all 5 Comments See all 5 5 Comments reply Show 2 previous comments Rupendra Choudhary commented Jul 2, 2017 reply Follow Share yes, it is. 0 votes 0 votes rahul sharma 5 commented Jul 2, 2017 reply Follow Share Can you once check nitish comments below for inflection point? 0 votes 0 votes Rupendra Choudhary commented Jul 2, 2017 reply Follow Share 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 votes 0 votes Please log in or register to add a comment.
0 votes 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 See all 8 8 Comments reply Show 5 previous comments joshi_nitish commented Jul 1, 2017 reply Follow Share sorry, i had seen only latter part of qsn where you have written one minima and two maxima. 0 votes 0 votes rahul sharma 5 commented Jul 1, 2017 reply Follow Share 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 votes 0 votes joshi_nitish commented Jul 1, 2017 reply Follow Share 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 votes 0 votes Please log in or register to add a comment.