Which of the following function is not differentiable at `x=0?` `f(x)=min{x ,sinx}` `f(x)={0,xgeq0x^2,x<0 `f(x)= x^2 sgn(x)

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

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

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).

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

Show that the following functions are not differentiable at the indicated value of x. f(x)={{:(3x",", x lt 0), (-4x",", x ge 0):}, x=0

Determine whether the following function is differentiable at the indicated values. f(x)=xabs(x) at x=0