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What are the points of inflection, if any, of #f(x)=x^4/(x^3+6 #?

1 Answer

Dec 12, 2016

#(root(3)12, (2root(3)12)/3)#

Explanation:

#f''(x) = -(36x^2(x^3-12))/(x^3+6)^3#

An inflection point of #f# is a point on the graph of #f# at which the concavity changes.

#f''# changes signs at #x=root(3)12# and at #-root(3)6#

#-root(3)6# is not in the domain of #f#, so there is no point on the graph pf #f# with #x = -root(3)6#.

#root(3)12# is in the domain of #f#, and #f(root(3)12) = (2root(3)12)/3#

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