Which of the following function is not differentiable at `x=0?` `f(x)={(0 ,, xgeq0),(x^2 ,, x<0):}` , `f(x)=x^2sgn(x)`

Which of the following function is thrice differentiable at x=0?

Which of the following functions is differentiable at x = 0?

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)="x"|"x"|

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

Which of the following statements is true for the function f(x)={sqrt(x),xgeq1x^3,0lt=xlt=1(x^3)/3-4x ,x 0

Let g: R -> R be a differentiable function with g(0) = 0,,g'(1)!=0 .Let f(x)={x/|x|g(x), 0 !=0 and 0,x=0 and h(x)=e^(|x|) for all x in R . Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)) . Then which of the following is (are) true? A. f is differentiable at x = 0 B. h is differentiable at x = 0 C. f o h is differentiable at x = 0 D. h o f is differentiable at x = 0

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