Fatima K.

asked • 08/07/18# find the concavity of y'=4y-y^3

I cant find the concavity of this function but I found the increase/decreae and everything else.

More

## 1 Expert Answer

Richard P. answered • 08/07/18

Tutor

4.9
(766)
PhD in Physics with 10+ years tutoring experience in STEM subjects

If the second derivative is positive, the function is concave upward. If the second derivative is negative, the function is concave downward. The second derivative can be found by differentiating the given first order differential equation then substituting for y' . The result for the second derivative is found to be:

(4y - y

^{3}) ( 4 - 3 y^{2}) This has zeros at -2, - sqrt(4/3) , 0 , sqrt(4/3) , 2A graphing calculator shows that it is positive for y > 2 and negative for y < -2. It is positive for y between the first two zeros, negative between the the second zero and 0 , positive between 0 and the fourth zero and negative again between the fourth zero and 2.

Of course finding the x values corresponding to these intervals is not so easy.

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Mark M.

08/07/18