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Question

The function f(x)=2x21x4, x>0, decreases in the interval

A
[1, )
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B
(1, )
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C
(0, )
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D
[0, )
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Solution

The correct option is B (1, )
Given that, f(x)=2x21x4, x>0f(x)=2x21x4, x>0f'(x)=4x3+4x5=4(1x2)x5f'(x)=04(1x2)x5=0(1x2)=0x=1 or 1.and x5=0x=0x=1,0 and 1 are the critical points.
This can be represented on number line as

From the figure, f '(x) < 0 for x(1, ) where f(x) decreases.

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