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 ?

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- Jun 26th 2010, 11:24 AMascendancy523Question on monotonicity problem
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 ? - Jun 26th 2010, 11:45 AMUtherr
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 - Jun 26th 2010, 11:52 AMAlso sprach Zarathustra
Can solved either with l'Hopital's rule.

- Jun 26th 2010, 11:55 AMAlso sprach Zarathustra
My mistake! Sorry!

- Jun 26th 2010, 12:40 PMAckbeet
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. - Jun 27th 2010, 07:12 AMchisigma
- Jun 27th 2010, 03:13 PMascendancy523
- Jun 28th 2010, 05:21 PMAckbeet
You're very welcome. Have a good one!