Find the open intervals for which concavity is open upwards.
I set f''(x)=0
So when I test the points to the left & to the right, and in-between, the positive intervals are:
which is apparently wrong. Where did I mess up? Thanks!
Concave up if the second derivative is positive, concave down if the second derivative is negative. If the second derivative is zero, your usually (but not always) at a point where the concavity is changing from up to down or from down to up. (An example of the not always case is at the origin.)
Got it. Thanks.
However, this one is question has got me stumped.
I need to find the intervals where f is increasing and decreasing.
So I start by taking the first derivative:
since 0 is not in the natural domain, it is not a critical point right?
When I plug in points on a number line, it shows that my function is increasing on:
and decreasing on
This is wrong. Where did I mess up?