# Thread: Second Derivative Help

1. ## Second Derivative Help

Hey Guys!
why cant a point of inflection occur at (d^3y)/(dx^3) = 0

2. ## Re: Second Derivative Help

Originally Posted by billjyang
Hey Guys!
why cant a point of inflection occur at (d^3y)/(dx^3) = 0
It can – consider y = x^5 at the origin.

3. ## Re: Second Derivative Help

Originally Posted by billjyang
Hey Guys!
why cant a point of inflection occur at (d^3y)/(dx^3) = 0
$\noindent It can. If y = x^5 then \frac{d^3y}{dx^3} = 60x^2. If \frac{d^3y}{dx^3} = 0 then x = 0. And at x = 0 there is a point of inflexion on y = x^5.$

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