If f(x) = x^4 -5x^2 +4, for what values of x is the absolute value of f(x) not differentiable?

Answer 1

y = |x^4 - 5x^2 + 4|
= | (x^2 - 4)(x^2 - 1) |
= | (x+2)(x-2)(x+1)(x-1) |

I graphed it on Wolfram
http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%5E4+-5x%5E2+%2B4%7C%2C+-3%3C+x+%3C+3

Notice that there are cusps at the zeros of the corresponding non-absolute function

At a cups the slope cannot be determined.
So the function is not differentiable at
x = ± 1, ± 2