Inflection Points

[stadtaffe2]

Find all inflection points of Y=x^4 - 6x^3 +12x^2 + 3

I got as far as Y ' ' = 12(x^2 -3x +2)

I am a bit confused on the algebra he gave us in the review. The next step showed simplifying it further to 12(x-2)(x-1) = 0 with X= 1 and X= 2

Can someone please explain how he got this.

Thank you in advance.
=
Note: After looking this over, I just realized this is the chain rule. Is this correct? (x^2) -x -2x+2 = (X^2) - 3x +2?

 

[tkhunny]

You're kidding, right? Did you have algebra? It is a prerequisite.

y = x^4 - 6x^3 + 12x^2 + 3

y' = 4x^3 - 18x^2 + 24x

y" = 12x^2 - 36x + 24 = 12(x^2 - 3x + 2)

Okay, that looks good.

Points of inflection require y" = 0

x^2 - 3x + 2 = 0

Now, really, if you cannot factor this or solve this with the quadratic formula or SOMETHING, you need to drop calculus and go confess to your local mathematics faculty how you gamed the placement exam.