Find number of roots of f(x) where `f(x) = 1/(x+1)^3 -3x + sin x`

Find f'(0) where f(x) = |x+1|+|x-1| .

If f (x)= [{:( cos x ^(2),, x lt 0),( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where f (x) =f )|x|) is non-difierentiable.

if f(x) is differentiable function such that f(1) = sin 1, f (2)= sin 4 and f(3) = sin 9, then the minimum number of distinct roots of f'(x) = 2x cosx^(2) in (1,3) is "_______"

In f (x)= [{:(cos x ^(3),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.

In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0):} then find the number of points where g (x) =f (|x|) is non-differentiable.

Find a if f’ (a) =0, where f(x) =x^3- 3x^2 + 3x-1 .

If f(x-1)=f(x+1) , where f(x)=x^2-2x+3 , then: x=

Find f'(0)where f(x)=|x+1|+|x-1|.