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October 9th, 2011, 02:35 AM  #1 
Newbie Joined: Apr 2010 Posts: 24 Thanks: 0  Determining a differentiable function given conditions
I am really stuck on this question g is a differentiable function for all pos. values of x such that these 3 conditions are true i. g(1)=0 ii. tangent to the graph at x=1 is inclined at 45 degrees to the positive xaxis iii. d/dx(g(2x)) =g'(x) a) Determine value for g'(2) b) Prove that g(2x) = g(x) + g(2) Any help would be much appreciated 
October 9th, 2011, 03:21 AM  #2 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Determining a differentiable function given conditions [color=#000000]From the second clue, and from the third for x=1, . Also, , for x=1 we get , so .[/color] 
October 9th, 2011, 03:43 AM  #3  
Newbie Joined: Apr 2010 Posts: 24 Thanks: 0  Re: Determining a differentiable function given conditions Quote:
 

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