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 functions have point of relative extremum at x=0?(A)f(x)=sin x-x

Which of the following functions is/are discontinuous at x=0?f(x)=sin((pi)/(2x)),x!=0 and f(x)=1

Which of the following function is not differentiable at x=0?f(x)=min{x,sin x}f(x)={[0,x>=0x^(2),x<0( c) f(x)=x^(2)sgn(x)

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

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

For which of the following functions f(0) exists such that f(x) is continuous at x=0f(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) 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

Find the one-sided limits of the following functions as x to 0 (a) f(x)=(1)/(2-2^(1//x)) (b) f(x)=e^(1//x) . (c ) f(x)=(|sin x|)/(x)

Investigate the following functions for an extremum at the point x = 0: f(x) = {:{(e^(1//x)", if "x !=0 ),(0", if "x=0):}