×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

How do you determine the concavity for #f(x) = x^4 − 32x^2 + 6#?

1 Answer
Apr 17, 2015

The concavity of a function is the sign of its second derivative.
If, in a set, it is positive, than the concavity is up, if negative the concavity is down, if it is zero, there could be an inflection point there.

So:

#y'=4x^3-64x#

#y''=12x^2-64#,

than

#12x^2-64>0rArrx^2>64/12rArrx^2>16/3rArr#

#x<-4/sqrt3vvx>4/sqrt3#, or , better:

#x<-4/3sqrt3vvx>4/3sqrt3#. In this set the function has concavity up, in the complementary set it has concavity dawn, in #+-4/3sqrt3# there are two inflection points.