Let f(x) = 3+4x-x^{3}. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

Question

1. f is increasing on the intervals?
2. f is decreasing on the intervals?

Answer 1

f is increasing where f' is positive

f' = 4-3x^2
So, where is 4-3x^2 > 0?

similarly for decreasing.

max/min where 4-3x^2 = 0