differentiable function

May 2008
400
82
Ottawa, Canada
suppose that f is a differentiable function with the derivative f'(x)=(x-1)(x+2)(x+3). determine the values of x for which the function f is increasing and the values for x for which the function is decreasing
 
Oct 2007
722
168
Should just be a simple case of determining f'(x) near 1,-2 and -3.

I imagine there's an easier or probably a more rigorous approach but just test a value in each of the intervals \(\displaystyle (-\infty, -3)\), \(\displaystyle (-3,-2) \), \(\displaystyle (-2,1)\), \(\displaystyle (1,\infty)\)