How can I test the condition and stability of the following function, for values $x=0$, $x=0.25$ and $x=10^{-5}$? $$ f(x) = \frac{1-cos(2x)}x $$ What should one do here? For condition, I think I should do the following: $$ K = \left|\frac{f'(x)}{f(x)} \cdot x\right| $$ and check if it's $>> 1$ or $< 10$.
1) Am I right for the condition? And how to check for that $x$ values given above? If not, how would be the right way?
2) How to check the stability also for that values?
Thank you in advance!!