Find the intervals on which f is increasing and the intervals on which it is decreasing.

Question

f(x)= -x^3 -8x

Answer 1

The derivative is -3x^2 - 8 <= -8 for all x

It is decreasing on (-∞, ∞)

More generally, functions with all terms of odd degree and all coefficients of the same sign will have no critical values and will be always increasing if signs are positive and always decreasing if signs are negative.