# For what values y is y(t) increasing/decreasing?

1. Feb 6, 2013

### Duderonimous

1. The problem statement, all variables and given/known data

y'=y$^{3}$-y$^{2}$-12y

For what values of y is y(t) increasing and for what values is it decreasing?

2. Relevant equations

3. The attempt at a solution

I think you take the second derivative and equal it to zero to figure out the inflection pints right and then Im not so sure from there.

y''=3y$^{2}$-2y-12

0=3y$^{2}$-2y-12

y=$\frac{2\pm2\sqrt{37}}{6}$

Am I correct in this approach? I dont think I am.

2. Feb 6, 2013

### skiller

For y to be either increasing or decreasing, you just need to look at whether y' is positive or negative, so the original equation gets you half-way there already - no need to differentiate again.

Try to factorize the RHS and it should become clear.

3. Feb 7, 2013

### rude man

You also need to take y''. Solving for y' = 0 just gets you the values of y for which the slope is zero. To also learn whether those points are (relative) minima or maxima requires taking y'' and substituting the values of y for which y' = 0.

Yes, factor by all means.

4. Feb 7, 2013

Rubbish.

5. Feb 7, 2013

### rude man

I say! I think you're right!

Last edited: Feb 7, 2013
6. Feb 8, 2013

### HallsofIvy

Staff Emeritus
Odd that oay should be ruder than rude man and then rude man agrees with him! But oay is right- the second derivative is irrelevant. You are NOT asked to find "inflection points".

y'= y3- y2- 12y= y(y2- y- 12)= y(y- 4)(y+ 3), then if y< -3, all three factors are negative so y' is negative. If -3< y< 0 then y+3 is positive while y and y= 4 are both negative so y' is positive, etc.

But you would still need to find what values of t give those values of y.

Last edited: Feb 8, 2013
7. Feb 8, 2013

### rude man

I agree with hallsofivy. When you're wrong... admit it! And I do.

8. Feb 8, 2013

### skiller

Finding values of t wasn't in the question, though.
And I apologize for my sharp reply of "Rubbish". I think I'd just had a bottle of Chardonnay.

9. Feb 8, 2013

### rude man

No apology required! It was just that.

10. Feb 8, 2013

### Dick

Apt comment gracefully accepted and, shall I say, "wittily" replied to. I worry a lot less about rudeness when replying to somebody with 1600+ posts under their belt. I assume that's made them at least a little bit thick skinned. Nice exchange. I don't think there was any real rudeness intended and better yet, none recieved.