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

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

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

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

Show that the function f(x)=x^3/2 is not differentiable at x=0.

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]

Check the nature of the following differentiable functions (i) f(x) = e^(x) +sin xc,x in R^(+) (ii)f(x)=sinx+tan x- 2x,x in(0,pi//2)

Consider the following statements: 1. The function f(x)=|x| is not differentiable at x=1. 2. The function f(x)=e^(x) is not differentiable at x=0. Which of the above statements is/are correct ?

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for all x,y in R.f(x)!=0 Suppose that the function is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x)