1 votes 1 votes How to Calculate? f(x) is decrasing in $[3,\alpha ]$ then f(x) is continuous or not continuous on x=5? srestha asked Dec 28, 2016 srestha 637 views answer comment Share Follow See all 12 Comments See all 12 12 Comments reply dd commented Dec 28, 2016 reply Follow Share what is $\alpha$ and what is $f(x)$ ? 0 votes 0 votes srestha commented Dec 28, 2016 reply Follow Share f(x) is a function $\alpha$ actually infinity 0 votes 0 votes Pavan Kumar Munnam commented Dec 28, 2016 reply Follow Share answer is continuous right? 0 votes 0 votes srestha commented Dec 28, 2016 reply Follow Share no.. 0 votes 0 votes Pavan Kumar Munnam commented Dec 28, 2016 reply Follow Share all monotonic functions are continuous in there interval http://math.stackexchange.com/questions/103630/proving-continuity-with-monotonic-functions so it should be continuous 0 votes 0 votes Anusha Motamarri commented Dec 29, 2016 reply Follow Share if α<5 we cant say anything about the behaviour at x=5. may or may not be continuous. but if α>5 i think it should be continous. 1 votes 1 votes srestha commented Dec 29, 2016 reply Follow Share yes, go for detail plz 0 votes 0 votes Anusha Motamarri commented Dec 29, 2016 reply Follow Share oh thats infinity.. i was thinking its alpha if that is infinity i think it should be continous If f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I. means tangent should exist at each point. as its given that it is decreasing function, tangent exist at every point even at x=5. so it should be continous 0 votes 0 votes Pavan Kumar Munnam commented Dec 29, 2016 reply Follow Share If tangent exists it is differentiable at that point if it is differentiable then it is continuous 0 votes 0 votes Anusha Motamarri commented Dec 29, 2016 reply Follow Share yes. 0 votes 0 votes Habibkhan commented Dec 29, 2016 reply Follow Share It may or may not be .. We can have discontinuous graph still satisfying decreasing function property..As basic definition is : f(x) is strictly increasing if f(a) > f(b) for all a < b. f(x) is increasing if f(a) >= f(b) for all a < b. rather than in terms of f'(x).. 0 votes 0 votes srestha commented Dec 29, 2016 reply Follow Share Without graph if any other way to derive it Like with function Can u give an example if example possible for f(a) > f(b) for all a < b. 0 votes 0 votes Please log in or register to add a comment.