If <mstyle displaystyle="true" scriptlevel="0"> f ( x ) =

Nickolas Taylor

Nickolas Taylor

Answered question

2022-07-05

If f ( x ) = 1 π ( arcsin x + arccos x + arctan x ) + x + 1 x 2 + 2 x + 10 , , Then max value of f(x)

Answer & Explanation

behk0

behk0

Beginner2022-07-06Added 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
cooloicons62

cooloicons62

Beginner2022-07-07Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?