So if for example I had a function like the following $f(x) = x^4-2x^2$ in the interval $[\frac{-1}{3}, \frac{4}{3}]$. In order to find the global maxima or minima I'd take the derivative with respect to x giving $f'(x) = 4x^3 - 4x$. Then find the values at which this derivative is $0$. So my question is, for this example would 0 be the global maximum?
What if I changed the domain to $(0,1]$ for example. Would this global maximum no longer exist since it's not within the domain or would it?
& one final question if you amended the domain from the original part to $[\frac{-1}{3}, 2]$ would 0 still remain as the global maximum or would the new global maximum be at x=2 even though this isn't a region where there's a turning point? Thank you.