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 decreasing
If you meant f'(x) = (x-1)(x-+2)(x+3)
since the = symbol is on the + key, then it has zeroes at
x = -3, -2, 1
Clearly, f' < 0 for x < -3 and it changes sign at each of the other two zeroes.
so f(x) is decreasing on (∞,-3) U (-2,1)
and increasing on (-3,-2) U (1,∞)
extra credit: what if f'(x) were (x-1) (x-+2)^2 (x+3)