# Concavity and Points of Inflection!

• Jul 5th 2009, 04:36 PM
mvho
Concavity and Points of Inflection!
Have a few questions guys

1. Test \$\displaystyle f(x)=5x^4-9x^3+3\$ for concavity and inflection points.

**So, to find the inflection points, I know I need to apply the 2nd derivative test which I got: \$\displaystyle f(x)=60x^2-54x\$

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 \$\displaystyle 6x^3-(108)x^2+(630)x-2\$ 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
• Jul 5th 2009, 04:51 PM
mvho
For question#1, I think I may have got it...

So my 2nd derivative was : \$\displaystyle f''(x)=60x^2-54x\$

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?
• Jul 5th 2009, 04:56 PM
skeeter
Quote:

Originally Posted by mvho
For question#1, I think I may have got it...

So my 2nd derivative was : \$\displaystyle f''(x)=60x^2-54x\$

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
• Jul 5th 2009, 04:57 PM
mvho
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!