



 
Hi Ron, I want to illustrate with the function f(x) = (1/4) (x  1)^{2} (x + 2)^{3}. The xintercepts are 1 and 2 and these two intercepts divide the line into three intervals. To the left of 2 I chose x = 3. f(3) = (1/4) (3  1)^{2} (3 + 2)^{3} which is positive so the function is positive on the interval ∞ < x < 2. Between 2 and 1 I chose x = 0. f(0) = (1/4) (0  1)^{2} (0 + 2)^{3} which is negative so the function is negative on the interval 2 < x < 1. To the right of 1 I chose x = 2. f(2) = (1/4) (2  1)^{2} (2 + 2)^{3} which is negative so the function is negative on the interval 1 < x < ∞. Here is a sketch of the function. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 