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How do you find the inflection points of the graph of the function: #y=1/3x^3#?

1 Answer

Nov 1, 2015

#(x,y)=(0,0)# is an inflection point.

Explanation:

#y=1/3x^3#

#frac{d^2y}{dx^2}=2x#

At inflection point, second derivative must be zero, which occurs at #x=0#.

#frac{d^2y}{dx^2}|_{x=0}=2(0)=0#

Now, do the first derivative test.

#frac{dy}{dx}=x^2# changes from positive to zero to positive in a small neighborhood around #x=0#. #x=0# is an inflection point.

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