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If f(x)=2 x cot ^(-1)x + log (sqrt(1+x^2...

If `f(x)=2 x cot ^(-1)x + log (sqrt(1+x^2)-x ` then f(x)

A

increases on R

B

decreases in `[0,oo)`

C

neither increasing nor decreasing in `(0,oo)`

D

none of these

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The correct Answer is:
A
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OBJECTIVE RD SHARMA-INCREASING AND DECREASING FUNCTIONS-Exercise
  1. Which of the following functions is not decreasing on (0,pi//2)?

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  2. If f'(x) = g(x) (x-a)^2, where g(a) != 0 and g is continuous at x = a,...

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  3. If f(x)=2 x cot ^(-1)x + log (sqrt(1+x^2)-x then f(x)

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  4. The function f(x)=log (1+x)-(2+x) is increasing in

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  5. On which of the following intervals in the function f(x)=2x^2-log|x|,x...

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  6. If the function f(x)=(Ksinx+2cosx)/(sinx+cosx) is strictly increasing ...

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  7. The function f(x)=(asinx+b cosx)/(c sinx+d cos x) is decreasing, if

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  8. If f(x)= kx^3-9x^2+9x+3 is increasing on R then

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  9. The values of a for which the function (a+2)x^3 - 3x^2 + 9ax-1 decreas...

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  10. The function y=x^3-3x^2+6x-17

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  11. The interval in which the function x^3 increases less rapidly than 6x^...

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  12. The interval in which the function f(x)=sin x-cos x -ax +b decreases f...

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  13. The function y=cot^(-1) x- log (x+sqrt(x^2+1)) is increasing in

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  14. the function (|x-1|)/x^2 is monotonically decreasing at the point

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  15. Find the value of a in order that f(x)=sqrt(3)sinx-cosx-2a x+b decreas...

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  16. A function is matched below against an interval where it is supposed t...

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  17. A condition for a function y=f(x) to have an inverse is that it should...

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  18. Let g(x)=f(x) +f'(1-x) and f''(x) lt 0 ,0 le x le 1 Then

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  19. The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decrea...

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  20. f(x)=(e^(2x)-1)/(e^(2x)+1) is

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