The function we are examining is f(x) = -x^3 - 8x^2 + 16 over the interval between -8 and -3. We want to find the maximum and minimum values of this function over the given interval.
Finding the maximum and minimum values of a function usually involves finding its derivative, and then setting it equal to zero in order to locate the x-values at which the function reaches its peak and valley, known as turning points. However, according to the question specification, we do not need to make these calculations.
Instead, the question provides us with the results which state that the minimum value of the function over the interval is -59.843 and the maximum value is 16.
So, over the interval from -8 to -3, the function f(x) = -x^3 - 8x^2 + 16 reaches its highest point at 16 and its lowest point at -59.843. This means that for any x value between -8 and -3 that you plug into this function, the result will never be greater than 16 or less than -59.843.