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Nickolas Taylor 2022-07-05 Answered
If f ( x ) = 1 π ( arcsin x + arccos x + arctan x ) + x + 1 x 2 + 2 x + 10 , , Then max value of f(x)
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Answers (2)

behk0
Answered 2022-07-06 Author has 14 answers
The domain should be x [ 1 , 1 ]
We have
f ( x ) = 1 π ( π 2 + arctan x ) + x + 1 x 2 + 2 x + 10
so
f ( x ) = 1 π ( 1 + x 2 ) + 9 ( x + 1 ) 2 ( x 2 + 2 x + 10 ) 2
This is positive because of ( x + 1 ) 2 4
Since f(x) is increasing, the answer is f ( 1 ) = 47 / 52
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cooloicons62
Answered 2022-07-07 Author has 4 answers
For x [ 1 , 1 ]
f ( x ) = 8 2 x x 2 ( 10 + 2 x + x 2 ) 2 + 1 π ( 1 + x 2 ) > 0
So, f is increasing in [ 1 , 1 ]. Thus, the maxima is taken at x=1. Plugging that in, the maxima is
f ( 1 ) = 1 π ( π 2 + π 4 ) + 2 13 = 3 4 + 2 13 = 47 52
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