Draw the graph of `y=(x+1)^(2//3) + (x-1)^(2//3)`

Explanation

We have `y=f(x) = (x+1)^(2//3) + (x-1)^(2/3)`
Domain of the function is R.
Also the curve never intersects the x-axis.
`f(x) = f(-x)`, so the function is even and hence the graph is symmetrical about the y-axis.
`f^(x)=2/3(x+1)^(-1/3)+2/3(x-1)^(-1/3)`
`=2/3(1/(x+1)^(1//3) +1/(x-1)^(1//3))`
`=2/3((x+1)^(1//3)+(x-1)^(1//3))/((x+1)^(1//3)(x-1)^(1//3))`
Critical points are `x=-1,0,1`.
`f^(')(x)` does not exist at `x=-1` and `x=1`, hence the function is non-differentiable at these points.
`f^(')(0)=0`
Sign scheme of `f^(x)` is as shown in the following figure.

`f(1)=f(-1)=2^(2//3)`
`underset(x to +-infty)"lim" [(x+1)^(2//3)+(x-1)^(2/3)]= infty`
Thus, the graph of the function is as follows: