Let #f(x)= sqrt(|x^3+1|)#. How to show that #f(x)# is not differentiable at #x=-1#?
1 Answer
Oct 20, 2017
Please see below.
Explanation:
Quick and maybe sketchy
The left and right derivatives at
(Specifically, the right derivative increases without bound and the left decreases without bound as
More detailed
Using the definition of
Look at the limit from the right:
or the limit from the left:
to see that the two-sided limit cannot exist.