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
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) $, $\displaystyle (-2,1)$, $\displaystyle (1,\infty)$