522 views
1 votes
1 votes
The interval in which $f(x) = \cot^{-1}x + x$ increases, is

(a) $R$

(b)$(0,\infty )$

(c)$R-[n-\pi]$

(d)None of these

1 Answer

Best answer
2 votes
2 votes

F(x) is increasing function if F'(x) >=0 (non negative)

here F'(x) =-1/(1+x2) + 1

= x2/(1+x2)

which is always greater than or equal to 0 (means non negative)

becoz both x2 >=0 and (1+x2 ) > 0 

(we know square of the number always non negative )

so here F(x) is increasing for all real number

selected by

Related questions

0 votes
0 votes
2 answers
1
kabilan45 asked Nov 25, 2021
504 views
Calculus looks difficult for me. Any resources to learn calculus for GATE
0 votes
0 votes
0 answers
3
sripo asked Dec 26, 2018
1,169 views
https://www.youtube.com/watch?v=tyiQLindzCEThis is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
0 votes
0 votes
1 answer
4