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Let g(x)=(2x-x^(2))^((1)/(log(10)(2x-x^(...

Let `g(x)=(2x-x^(2))^((1)/(log_(10)(2x-x^(2))))`. The value of x for which f' vanishes may be

A

1

B

`(1)/(2)`

C

`(3)/(2)`

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`g(x)=(2x-x^(2))^(log_((2x-x^(2))^(10)))=10`
`:.g(x)=10rArrg'(x)=0AAx in D_(g)`
`{:(2x-x^(2)gt0,and,2x-x^(2)!=1,),(x^(2)-2xlt0,,(x-1)!=0rArrx!=1, . . . . . (1)),(x(x-2)lt0,,,),(x in(0,2),,. . . . .(2),):}`
(1) and (2) `rArrx in(0,2)-{1}`.
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