Hello, and welcome to FMH!I really need help solving this inequality
1/(x-2) + (1/3) * x^3 - 1 > 0
Thanks in advance
What I get is:That is exactly what i have a problem with , the best i got is
but im not sure if this is any good. Thanks for replying quickly.
Okay, now that I know what level you're at, I would advise you to find the extrema of our numerator. Equate its first derivative to zero, and using Descartes' Rule of Signs, how many real roots are there?I am now, im supposed to find extrema of
I don't speak english that well, can you just explain how to do this so i can try it on my own?
Normally, one would try to factor or find the 4 roots of the numerator to see if there are additional critical points, in addition to the critical point in the denominator.We are finding the root of the derivative of the quartic, which is a cubic.
Using W|A, I find the one real root is approximately:We have:
There is only 1 sign change, so this means there will be one real root. To determine this one real root, I would use a numeric root finding technique to get an approximation. Are you familiar with the Newton-Raphson method? Depending on your professor, you may simply be allowed to use a CAS (computer algebra system) like WolframAlpha to approximate the root. What do you find?