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Question

Let g:[1,6][0,] be a real valued differentiable function satisfying g(x)=2x+g(x) and g(1)=0, the maximum value of g cannot exceed.

A
ln 2
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B
ln 6
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C
6 ln 2
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D
2 ln 6
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Solution

The correct option is A ln 2
f(x)=(x) for x0
= x=0
g(x)=2x+g(x)
g(x)+x=2g(x)g(x)=2g(x)x
g(1)=21=2g(x)=102g(x)x
=2ln[g(x)]x22
=2ln(2)12
Value of g(x) will never be greater than ln2

1453900_768776_ans_c4db053aec334be3a37cb88b3cee47b0.png

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