Does anyone have an example of a function such that f'(x) exists everywhere, but limf'(x) as x approaches 0 does not?
Thanks in advance!
The Attempt at a Solution
I was thinking something along the lines of f(x) = (2x^5 + 5x^2)/x^11
Since then f'(x) = (10x^4 + 10x) / 11x^10
and limf'(x) as x approaches 0 does not exist since 11(0)^10 = 0 and you cannot divide by 0. However, I realized that that means that f'(x) does not exist everywhere since limf'(x) doesn't exist as x approaches 0, that implies that f'(0) does not exist.