Finding limit supremum While finding the limit supremum of $5x\cos(πx) - x^2$, the book says it is $-\infty$. But this function is bounded above. Shouldn't it's supremum be the lowest upper bound(which is 6). Why does it say it's supremum is $-\infty$ ?

Note that $f(x)=5x\cos(πx) - x^2$ is continuos and

* $\lim_{x\to \pm \infty} f(x)=-\infty$



then by EVT the function has maximum and is bounded from above.