In which of the following cases, the function f(x) has vertical tangent at x = 0 ?
(ii) `f(x)=sgnx`

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? (i) f(x)=x^(1//3)

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? f(x)=x^(2//3)

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? f(x)=sqrt(|x|)

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? (v) f(x)={{:(0","," if "xlt0),(1","," if "xge0):}

For which of the following functions does f(x) f(2 - x) ?

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

Prove the each of the following function is differentiable at x=0. (i) f(x) = cos|x| (ii) f(x) = x|x| (iii) f(x)=|x^(3)|(iv) f(x) =(x)/(1+|x|)

For which of the following functions f(0) exists such that f(x) is continuous at x=0 f(x)=1/((log)_e|x|) b. f(x)=(cos((sin|x|)/x)) c. f(x)=x sin(pi/x) d. f(x)=1/(1+2^(cot x))

In which of the following function, range is not singleton set f(x)=[x]+[-x] (b) f(x)={x}+{-x} f(x)=|sgn(x)| (d) f(x)=[sqrt(x-[x]) where [x],{x},a n dsgn(x) are greatest integer function, fractional part function and signum function respectively.

Which of the following function has point of extremum at x=0? f(x)=e^(-|x|) f(x)="sin"|x| f(x)={x^2+4x+3,x<0-x , xgeq0 f(x)={|x|,x<0{x},0lt=x<1 (where {x} represents fractional part function).