Plug in maximum value of x (3) and see what you get. The maximum value of the expression when plugged in is C.
[tex]3^3-3\cdot3+5=C[/tex]
[tex]27-9+5=C\implies 23=C[/tex]
Now that means,
[tex]x^3-3x+5\leq 23[/tex] for any x in [tex][0,3][/tex]
Hope this helps :)
