Re: DSE 2012 paper discussion-Please join

Posted by Granpa Simpson on May 20, 2014; 8:50am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2012-paper-discussion-Please-join-tp7590218p7590245.html

47) Given, g(x)= lim(t→x)[f(c+t)-f(c+x) ]/(t-x),
Let t-x=h,
so, g(x)=lim(h→0)[f(c+x+h)-f(c+x)]/h,
or g(x)=f'(x+c) [By using first principle of derivative].
Again since f(x) is concave in x, sol clearly it will be concave in (x+c) too.
so g'(x)=f''(x)<=0.
So clearly g(x) is decreasing in x.