The first thing we need to do is evaluate the function at its endpoints.
[tex]f(-2)=-1\\\\f(5)=-183[/tex]
Then, we need to find the critical points to find if the stationary points give the absolute min/max values.
[tex]f'(x)=12x^2 - 36x-48=0\\\\x^2 - 3x-4=0\\\\(x-4)(x+1)=0\\ \\ x=-1, 4[/tex]
[tex]f(-1)=33\\\\f(4)=-217[/tex]
So, the absolute maximum is 33 and the absolute minimum is -217
