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).

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|

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

Which of the following function from Z to itself are bijections? f(x)=x^3 (b) f(x)=x+2 f(x)=2x+1 (d) f(x)=x^2+x

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|)

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

Discuss the extrema of the following functions (i)f(x)=|x|,(ii)f(x)=e^(-|x|),(iii) f(x)=x^(2//3)

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

Which of the following is true about point of extremum x=a of function y=f(x)? At x=a , function y=f(x) may be discontinuous. At x=a , function y=f(x) may be continuous but non-differentiable. At x=a ,function y=f(x) may have point of inflection. none of these