# We have #f:RR->RR,f(x)=|x|root(3)(1-x^2)#.How to find maximum domain of differentiability?

##### 1 Answer

May 24, 2017

See below.

#### Explanation:

# = root(3)(1-x^2) - (2x^2)/(3(1-x^2)^(2/3))#

# = (3(1-x^2)-2x^2)/(3(1-x^2)^(2/3))#

# = (3-5x^2)/(3(1-x^2)^(2/3))# .#" "# For#x != +-1#

So,

And

Checking the "joint" of the "hinge" of the two parts, we see that the right derivative at

Finally, here is the graph of the function: graph{y=(1-x^2)^(1/3)absx [-2.433, 2.436, -1.215, 1.217]}