What is the interval notation for -4(x+9)^3(x-11)^4(x+6)>0
-4(x+9)^3(x-11)^4(x+6)>0
Since the (x-11)^4 is always positive for x≠11, and the -4 is always negative, and n^3 has the same sign as n, you really just have to worry about
(x+9)(x+6) < 0
In between -6 and -9, x+9 > 0 and x+6 < 0, so the interval you need is (-9,-6)
Or, you can do a little root analysis. The graph crosses the x-axis for roots of odd multiplicity, and is tangent at roots of even multiplicity.
Since for large negative values of x (say, -100) the factors are -4(-)(+)(-) the functions is negative.
It crosses to positive at x = -9
it crosses to negative at x = -6
It touches y=0 but then stays negative at x=11
So, only in (-9,-6) is the function positive