Maybe try factoring each quadratic with the purpose of cancellation. Otherwise your stuck with the quotient rule.
Hello, I am trying to differentiate this function so I work out where it is increasing or decreasing.
What is the best procedure to do this. I tried using quotient rule but it seemed very laborious. Is there a better way ?
2x^2+x-1 / x^2+x-2
Thanks for any help.
thank you. I have tried to continue to simplify this derived function so that I can work out it's roots.
I can see I could split it and cancel one of the (x^2+x-2) factors, but that is as far as I can get.
I really am stuck with this one. Any help proceeding would be great.
as stated by AsZ, expand the numerator and combine like terms ... in other words, do the grunt work algebra and finish simplifying the numerator.
You'll end up with a quadratic in the numerator that won't factor, so you'll need to complete the square or use the quadratic formula to find where the derivative equals 0.
my grunt work gives me:
x^2-6x-1 / x^4+2x^3-3x^2-4x+4
I equated the numerator to zero to find the roots. That gave me roots at 6.16 and -0.162 however looking at a graph of 2x^2+x-1 / x^2+x-2 that cannot be correct.
I double checked but to no avail.
If anyone can spot my error that would be appreciated.