So here's my problem:
Find where the given function is increasing and decreasing.
So
So to find the split points would I solve and ?
Solve f'(x) = 0, this means which is a 2nd degree polynomial with a = 2 > 0, this means is negative between its roots [x1, x2] and positive for the rest (-inf, x1) U (x2, +inf), if a < 0 the sign would be reversed.
if f`(x) < 0 then f(x) is decreasing on that interval, f`(x) > 0 increasing on that interval
i forgot to mention is always positive so it doesn't interfere with the sign of your derivative
I think you have a sign error in your derivative. For the quotient rule, I always use this mnemonic:
"lo dee-hi minus hi dee-lo over the square of what's below". That is,
.
If you compare this with how you took your derivative, I think you'll see the error. And this error will affect your results, because all your answers will be reversed from what they should be.