Re: DSE DOUBT

Posted by Sris on Jun 09, 2015; 3:48am
URL: http://discussion-forum.276.s1.nabble.com/DSE-DOUBT-tp7597512p7597521.html

DSE DOUBTS....PLZ SOLVE

1. WHICH OF THE FOLLOWING IS QUASI CONVEX (GIVEN f:R TO R)
A)f(x)= x^2
b) f(x)=cosx
c)f(x)=e^-x
d)f(x)=1/x if x not equal to zero and f(x)=0 if x=0

how to check for quasi convexity...

2.consider a strictly decreasing and differenciable and f:R to R. denote the derivative of f at x belonging to R by Df(x).which of the following is true
a) Df(x)>0 for some x belonging to R
B) Df(x)=0 for some x belonging to R
c) Df(x)=0 for some x belonging to (a,b) where a=0 for some x belonging to R

how to solve this

3. if f: R^n to R is twice differenciable ,concave and homogenous of degree 1 then the hessian matrix of f is
a) negative definite
b)positive definite
c)singular
d)non- singular
 
how to solve this...n from where shud i read to get hold of the topics asked in all d above Q