5 votes 5 votes $The\ maximum\ value\ of\\f(x)\ =\ 2x^3-9x^2+12x-3\ in\ the\ interval\ 0<=x<=3\ is\ $ _____________________ Calculus engineering-mathematics calculus maxima-minima + – Tuhin Dutta asked Jan 4, 2018 Tuhin Dutta 1.2k views answer comment Share Follow See all 17 Comments See all 17 17 Comments reply vijay_jr commented Jan 4, 2018 reply Follow Share is it 6? 1 votes 1 votes akash.dinkar12 commented Jan 4, 2018 reply Follow Share the max value will be 6.. 0 votes 0 votes vishal chugh commented Jan 4, 2018 reply Follow Share Got the value 6 but if we do by differentiation method Maxima will occur at x=1 and the value obtained will for x=1 will be 2. So how do we know that maximum can occur at any other value also? 0 votes 0 votes saxena0612 commented Jan 4, 2018 reply Follow Share ........................................................................................................................ 0 votes 0 votes vijay_jr commented Jan 4, 2018 reply Follow Share When we say f(x) is maximum at x=a, we mean that it is greatest in neighborhood of a i.e [a-h,a+h] 0 votes 0 votes srestha commented Jan 4, 2018 reply Follow Share points are -2 and -1 So, inside 0 to 3 no maximum value possible right? 0 votes 0 votes akash.dinkar12 commented Jan 4, 2018 reply Follow Share stationary points 2 and 1 only... 0 votes 0 votes srestha commented Jan 4, 2018 reply Follow Share 2 is not possible at all 0 votes 0 votes srestha commented Jan 4, 2018 reply Follow Share 1 possible but with solution we are not getting it 0 votes 0 votes akash.dinkar12 commented Jan 4, 2018 reply Follow Share let me know if anything is wrong!!! 2 votes 2 votes srestha commented Jan 4, 2018 reply Follow Share yes , I done a mistake So, they are asking for maximum value which is not possible for 2 It is only possible for 1 right? 0 votes 0 votes akash.dinkar12 commented Jan 4, 2018 reply Follow Share yes for x= 2 function will have minimum value.. 0 votes 0 votes srestha commented Jan 4, 2018 reply Follow Share yes, so 1 is correct ans 0 votes 0 votes akash.dinkar12 commented Jan 4, 2018 reply Follow Share for x =1, we didn't have a maximum value, actually, they have given open interval range and for finding maximum we have to check those values too.That;s why i m checking at x=3 also which gives us maximum value as 6 1 votes 1 votes Tuhin Dutta commented Jan 4, 2018 reply Follow Share Ans is 6. Here we need to check all the values including 0 to 3 that at which value max occurs. Critical or stationary points(1,2) doesn't give the maximum but at 3 we get the maximum value of 6. f(0) = -3 f(1) = 2 f(2) = 1 f(3) = 6 0 votes 0 votes LeenSharma commented Jan 9, 2018 reply Follow Share In the given interval at the x=3 function will maximum value (6). 0 votes 0 votes pradeepchaudhary commented Jan 3, 2019 i moved by Lakshman Bhaiya Jan 3, 2019 reply Follow Share answer is 6 ,which is at x=3 0 votes 0 votes Please log in or register to add a comment.