Column I Column II
f(x)=x^2logx f(x) has one point of minima
`f(x)=x(log)_e x`
q. `f(x)` has one point of maxima
`f(x)=(logx)/x` r. `f(x)` increase x in (0,e)
`f(x)=x^(-x)` s. `f(x) decrease x in (0,1/e)`

If f(x) =|log_(e)|x||, then f'(x) equals

Discuss the differentiability of f(x)=|(log)_e|x||

Find the range of f(x)=(log)_e x-((log)_e x)^2/(|(log)_e x|)

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

If f(x)=(log)_e((x^2+e)/(x^2+1)) , then the range of f(x)

Iff(x)=sin(logx) then f(xy)+f( y x ​ )−2f(x)cos(logy) is equal to

Column I: Function, Column II: Period f(x)=(log)_3(5_(4x)-x^2) , p. Function not defined f(x)=(log)_3(x^2-4x-5) , q. [0,oo] f(x)=(log)_3(x^2-4x+5) , r. (-oo,2] f(x)=(log)_3(4x-5-x^2) , s. R

Column I: Function, Column II: Value of x for which both the functions in any option of column I are identical f(x)=tan^(-1)((2x)/(1-x^2)),g(x)=2tan^(-1)x , p. x in {-1,1} f(x)=(log)_(x2)25a n dg(x)=(log)_x5 , q. x in (-1,1) f(x)=sec^(-1)x+cos e c^(-1)x ,g(x)=sin^(-1)x+cos^(-1)x , r. x in (0,1)

Let a function f be defined by f(x)=(x-|x|)/x for x ne 0 and f(0)=2. Then f is