- #1
SixBooks
- 5
- 0
The function f: R → R is: f(x) =
(tan x) / (1 + ³√x) ; for x ≥ 0,
sin x ; for (-π/2) ≤ x < 0,
x + (π/2) ; for x < -π/2
_
For -π/2 I would say it is not differentiable since both π and 2 are constants and you can not vary a constant.
For 0, I would derivate it by using the first function - (tan x) / (1 + ³√x) - and just replace x for 0. It gives me 0 as result. If x ≠ 0, the result could also be ≠ 0.
From here I can't go further...
(tan x) / (1 + ³√x) ; for x ≥ 0,
sin x ; for (-π/2) ≤ x < 0,
x + (π/2) ; for x < -π/2
_
For -π/2 I would say it is not differentiable since both π and 2 are constants and you can not vary a constant.
For 0, I would derivate it by using the first function - (tan x) / (1 + ³√x) - and just replace x for 0. It gives me 0 as result. If x ≠ 0, the result could also be ≠ 0.
From here I can't go further...