Find the intervals on which the function f(x) = (x^2 + 4x + 4)(x - 1) is increasing or decreasing. Apply the first derivative test to identify all relative extrema.
Good work! That's perfect so far. Now I find the best way to test for critical points is to draw a number line and mark the two points you found. Those points mark a slope of 0, or similarly at those points f'(x)=0. So the regions inbetween these points there will be a consistent positive or negative slope. Use test points inbetween your critical points to determine the slope for that region. If the slope changes from positive to negative or from negative to positive before and after a critical point, you then have a relative extrema.