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 ? (ii) f(x)=sgnx

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):}

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))

If f(x)=cosx and g(x)=2x+1 , which of the following are even functions? I. f(x)*g(x) II f(g(x)) III. g(f(x))

Which of the function is non-differential at x=0? f(x)=|"x"^3|

Which of the following function/functions has/have point of inflection? f(x)=x^(6/7) (b) f(x)=x^6 f(x)=cosx+2x (d) f(x)=x|x|