Increasing and decreasing functions...?

Question

Find the intervals on which f increases and the intervals on which f decreases:

(a). f(x) = x (x + 1) (x + 2)

(b). f(x) = x / (1 + x^2)

(c). f(x) = x + sin x, 0<=x<=2pi

Explain your work. Thanks! :)

Answer 1

If this is for a calculus class, then just take the derivative of each function, and see where it's positive (increasing f) and where it's negative (decreasing f).