Thread: Concavity and Points of Inflection!

Have a few questions guys

1. Test for concavity and inflection points.


**So, to find the inflection points, I know I need to apply the 2nd derivative test which I got:

From here, I set the 2nd derivative =0 which I am having a hard time with.... I think I need to factor somewhere but I don't see it (well its not obvious to me hence I am here. ) For Concavity, you just plug in numbers that are bigger or smaller than your critical # to find where its concavity correct?


And can someone help me with the concavity question?

The Second question:

2. Test the function for relative maximum and minimum.

** I applied the second derivative test again to try and find the critical points: f''(x)=24x-216

Which my textbook tells me is wrong.

As usual, TIA

For question#1, I think I may have got it...

So my 2nd derivative was :

But I've just noticed I can factor out a 3x so I have now:

f''(x)= 3x(20x-18)=0
20x=18
x=9/10

So my critical point would be x=9/10?

Hurrah? Or no Hurrah?

Originally Posted by mvho

For question#1, I think I may have got it...

So my 2nd derivative was :

But I've just noticed I can factor out a 3x so I have now:

f''(x)= 3x(20x-18)=0
20x=18
x=9/10

So my critical point would be x=9/10?

Hurrah? Or no Hurrah?

you forgot x = 0

Thanks, I'll plug away at the 2nd question now ( looking at it again, I think I need to apply the chain rule somewhere..). I realized that I posted this on the wrong sub forum. Can someone move this to the appropriate forum please?

Sorry!