Question:
The plot of function y=4x-x^4 appears to have two inflection points.
yet d^2y/dx^2 = -12x^2 = 0 ;x=0 only solution, hence only one inflection
point. Please explain discrepancy.

Replies:
The function graph has no inflection point, since the second derivative
does not change sign at x = 0. This is a common error of analysis
using derivatives --- zeros of the second derivative must be tested
further before they can be classified as inflection points. It seems
that you should check carefully what has been plotted --- if a grapher
has been used --- find a better one.

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