# Finding concavity

1. Apr 19, 2004

### ACLerok

http://www.eden.rutgers.edu/~cjjacob/images/calc.gif [Broken]

I am given this problem to do but I'm not absolutely sure how to get through it. The way I would do is to find y' in terms of x's and y's and then plugin the point (1,2) and then take the derivative again and see if y'' is positve (curve up) or negative (curve down). Is this the best way to go about this problem or is it completely wrong or what?

Last edited by a moderator: May 1, 2017
2. Apr 19, 2004

Yes. Concavity is determined by the second derivative.

So implicitly differentiate twice and get an expression for d^2y/dx^2 in terms of x and y. Then plug in (1,2).

And whatever you do, ignore that ugly-looking expression for y(x)! That will make your life very, very, very miserable.

Last edited: Apr 19, 2004
3. Apr 19, 2004

### ACLerok

I calculated the first derivative and got 15x^(2)y+5x^(3)y'-3y^(2)-6xyy'+3y^(2)y'=0. is this correct and if so, what do i do after this? express in terms of y'?

4. Apr 19, 2004