Asked by Erin
What is the interval notation for -4(x+9)^3(x-11)^4(x+6)>0
Answers
Answered by
Steve
-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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.