# DSE 2011 Q.24 Classic List Threaded 11 messages Open this post in threaded view
|

## DSE 2011 Q.24

 If a function F(x)= Integral a to b f(t)dt is increasing on an interval, then on that interval F is convex concave increasing decreasing  Answer key says convexBut consider the following figure, where a convex combination of points related to b and c lie outside the set. Shouldn't the answer be increasing? I don't understand, I might be wrong, could someone shed some light on how they did this? Open this post in threaded view
|

## Re: DSE 2011 Q.24

 Even i think the ans is wrong n shld b increasing....... For reference read condition here: http://tutorial.math.lamar.edu/pdf/Calculus_Cheat_Sheet_Derivatives.pdf
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 Ritu, the function f(t) in indeed convex, but the function F(x) is definitely not, because it is a closed set but doesn't satisfy the condition of convexity
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 In reply to this post by Khagesh Thanks Khagesh, that sheet clarified things. Maybe the answer key has an error.
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 In reply to this post by Khagesh if i m nt wrong ur thinking abt "convex set" rather than a "convex function"...the graph u have shown is depicting a convex function..
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 ok..i dnt kno then....sorry...
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 In reply to this post by ritu Hmm. I see what you mean Ritu... My only doubt is that f(t) is a convex function all right, I agree. But are we supposed to look at F(x) in the sense of a set or a function?
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 Hi Chinni.. :) F(x) is a function not a set. And the correct answer is Convex only. Option(c) i.e "increasin" can be ruled out using the following example> Consider f(t) = -2. Its an increasing and convex function but F(x) = -2x which is a decreasing function. :)
Open this post in threaded view
|

## Re: DSE 2011 Q.24

 Ohhhh.... Ya you're right!!!!! Thanks duck!!!!! You're a life-saver!!!On Thu, Jun 21, 2012 at 6:29 PM, duck [via Discussion forum] wrote: Hi Chinni.. :) F(x) is a function not a set. And the correct answer is Convex only. Option(c) i.e "increasin" can be ruled out using the following example> Consider f(t) = -2. Its an increasing and convex function but F(x) = -2x which is a decreasing function. :) If you reply to this email, your message will be added to the discussion below: http://discussion-forum.2150183.n2.nabble.com/DSE-2011-Q-24-tp7578446p7578466.html To unsubscribe from DSE 2011 Q.24, click here. NAML