Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x3 − 18x2 − 48x + 1, [−2, 5]

The given function is

We need to find the derivative.And the derivative is

Now we need to find the critical numbers, and for that we need to set f'(x) to 0 and solve for x, that is

Now we need to find the value of the given functions at the boundary numbers and the critical numbers.

So absolute minimum is -223 at x=4 and absolute maximum is 27 at x=-1 .