February 21st, 2012, 09:29 PM  #1 
Newbie Joined: Jan 2012 Posts: 23 Thanks: 0  3 doubts plz help!!
Kindly help me with the following 3 questions and please tell me how you arrived at the answer. Thanks in advance Let f and g be two differentiable functions on (0, 1) such that f(0) = 2, f(1) = 6, g(0) = 0 and g(1) = 2. Then there exists ? ? (0, 1) such that f'(?) equals (a) (1/2)g'(?), (b) 2g'(?), (c) 6g'(?), (d) (1/6)g'(?). If f(1) = 0, f'(x) > f(x) for all x > 1, then f(x) is (a) positive valued for all x > 1, (b) negative valued for all x > 1, (c) positive valued on (1, 2) but negative valued on [2,?). (d) None of these. For all x, y ? (0, ?), a function f: (0, ?) > R satisfies the inequality f(x)  f(y) ? cube(x  y). Then f is (a) an increasing function (b) a decreasing function (c) a constant function (d) None of these. 
February 22nd, 2012, 04:38 AM  #2 
Newbie Joined: Jan 2012 Posts: 23 Thanks: 0  Re: 3 doubts plz help!!
Someone please answer!!

February 22nd, 2012, 06:18 AM  #3  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond  Re: 3 doubts plz help!! Quote:
Quote:
 
February 22nd, 2012, 08:13 AM  #4 
Newbie Joined: Jan 2012 Posts: 23 Thanks: 0  Re: 3 doubts plz help!!
Thank you greg But I haven't got the 2nd question. We are just given that f'(x)>f(x) for all x>1.. how did you say that f'(1)>f(1)?? Please reply. And I would be very grateful to anyone who can help me with the 3rd question as well.. 
February 22nd, 2012, 08:30 AM  #5 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,898 Thanks: 1093 Math Focus: Elementary mathematics and beyond  Re: 3 doubts plz help!!
I made an error on that one, my apologies.


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