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Can you please check if the following solution is correct? if not please correct it.

 

asked in Calculus by Veteran (16.4k points) 15 135 252 | 251 views
maxima at x= -3

minima at x= 0

???
please no short messages! I din't get you what you want to ask, please ask in details then i will be able to answer
@kunal
Do we check local maxima/minima on end points?
maxima value occur  at x= -3

minima value occur  at x= 0

yes , it should be checked on endpoints also as square braces are given in the question .
I don't agree to this point! we don't check local maxima and minima on end points, however we check on end points in the case of absolute maxima/minima.

If you have any links to prove your point it will be a great help!

@vijaycs Please check this. I think it might be helpful for you. Just check the example towards the end. http://mathinsight.org/local_minima_maxima_refresher

Yes ur solution is fine @Vijay Thakur...@kunal chalotra at x = -3 , absolute maximum exists not local maxima exists..

@habib khan
what should be the answer of this question according you (B) or (D)
http://gateoverflow.in/41/gate2012_9

after calculating critical points we have differentiate second time to check local maxima and minima .rt habib??
Yes then we have 0 at x = 1 and > 0 at x = 0 ..So clearly x = 0 is a point of minima..But for x = 1 , we need to check further..
It should be  B) without any doubt as in case of local minima or maxima we do not consider the extreme points or points of discontinuity..

Only we check the points using derivatives..That is it..

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