Find the interval in which f(x) = log(1 + x) - x/(1 + x) is increasing or decreasing ?

Question

Find the interval in which \(\text{f(x)} = \text{log}(\text{1 + x})-\frac{\text{x}}{\text{1 + x}}\) is increasing or decreasing ?

Answer 1

We have

Critical points

Hence, f(x) increases in (0, ∞), decreases in (–∞, –1) U (–1, 0)