f’(x)>0,e^x- 1>； 0,e^x>； 1，x & gt0,

f '(x)& lt； 0,e^x- 1<； 0,e^x<； 1，x & lt0,

The increasing interval of f(x) is (0, +∞), and the decreasing interval is (-∞, 0).

3. The derivative function of cubic function is quadratic function, and the sign problem of quadratic function is well solved.

f’(x)>0,3-3x^2>； 0,x^2<； 1，- 1 & lt； x & lt 1;

f '(x)& lt； 0,3-3x^2<； 0,x^2>； 1, x<- 1, or x> 1;

The increasing interval of f(x) is (-1, 1), and the decreasing interval is (-∞,-1), (1, +∞).

4.

f'(x)=3x^2-2x- 1=(3x+ 1)(x- 1)，

F'(x)>0, x <-1/3, or x >1,

f '(x)& lt； 0，- 1/3 & lt； x & lt 1.

The decreasing interval of f(x) is (-1/3, 1), and the increasing interval is (-∞,-1/3), (1, +∞).

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