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f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+...

`f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)`

A

a) `f(x)` is increasing for all `x in R`

B

b) `f(x)` is decreasing for all `x in R`

C

c) `f(x)` is increasing in its domain

D

d) none of the above

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Single Option Correct Type Questions)
  1. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

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  2. Evaluate (n!)/((n-r)!) , when n = 8 , r = 6

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  3. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

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  4. Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi, Then, f(x) is

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  5. Evaluate (5!)/((5 - 2)!)

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  6. Maximum number of real solution for the equation ax^(n)+x^(2)+bx+c=0...

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  7. Maximum number area of rectangle whose two points are are x=x(0),x=p...

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  8. f(x)=-1+kx+k neither touches nor intecepts the curve f(x)= Iog x, then...

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  9. f(x) is a polynomial of degree 4 with real coefficients such that f(x)...

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  10. A curve whose concavity is directly proportional to the logarithm of i...

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  11. f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)

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  12. f (x)= {{:(3+|x-k|"," , x le k),(a ^(2) -2 + ( sin (x -k))/((x-k))"," ...

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  13. Let f(x) be linear functions with the properties that f(1) le f(2), f(...

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  14. If P(x) is polynomial satisfying P(x^(2))=x^(2)P(x)andP(0)=-2, P'(3//2...

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  15. Find the vertex and length of latus rectum of the parabola x^(2)=-4(y-...

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  16. Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

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  17. Prove that (9!)/((9 - 3)!) = 504

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  18. Evaluate (n!)/((n-r)!) , when n = 10 , r = 5

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  19. Let a(1),a(2),a(n) be sequence of real numbers with a(n+1)=a(n)+sqrt(1...

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  20. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

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