Find the infimum of the function $2x^3-9x^2+12x+5$ $X\le5$.
I think, there the infimum of the $2x^3-9x^2+12x+5$ in the $X\le5$ is -infinity since examining the plot of the function I can see that it goes to $-\infty$. However,I would like to understand if my reasoning is correct and how to find the infimum or supremum of the function more formally in general?