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October 9th, 2011, 02:35 AM   #1
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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 x-axis
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
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October 9th, 2011, 03:21 AM   #2
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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]
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October 9th, 2011, 03:43 AM   #3
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Re: Determining a differentiable function given conditions

Quote:
Originally Posted by ZardoZ
[color=#000000]From the second clue, and from the third

for x=1, .

Also,

, for x=1 we get , so .[/color]
thanks a lot
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