how do you find the inflection points for

.25x^4 - x^3 + 6?

I know that you find the first derivative which would be:

x^3 - 3x^2

And I think the second derivative is 3x^2 - 6x, and after setting that to 0, I got x=0 and x=6 for inflection points. This is one of the answers on the homework assignments but it also has another set of points....any ideas on where they are getting the other set of inflection points?

Question

how do you find the inflection points for 

.25x^4 - x^3 + 6?

I know that you find the first derivative which would be:

x^3 - 3x^2

And I think the second derivative is  3x^2 - 6x, and after setting that to 0, I got x=0 and x=6 for inflection points. This is one of the answers on the homework assignments but it also has another set of points....any ideas on where they are getting the other set of inflection points?

kkutie7 · Answer

your second derivative is right. From here you could do this x(3x-6) so x=0 and x=2. I hope you follow. From here You need to make a number line.|dw:1374466859593:dw|

anonymous · Answer

there are only two inflexion points for a fourth degree polynomial

anonymous · Answer

i guess i should say "at most two"

kkutie7 · Answer

Now use the point in between to plu|dw:1374466980579:dw|g into a table.