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[M2] m2 微分一問

m2 微分一問

dy/dx=slope   d^2y/dx^2= rate of change of slope

搵point of inflexion果陣d^2y/dx^2要=0  

d^2y/dx^2=0 係咩意思???slope無變??

   

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[隱藏]
d^2y/dx^2=0  means that the slope doesn't change at that point. (may be the case of concave up -->d^2y/dx^2=0--> concave down and vice versa)

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Point of inflexion requires the following:
1) Either "second derivative = 0" Or "second derivative undefined" at point x=c

AND

2) second derivative change sign around x=c

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PI is the point that is the point at which the concavity changes

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for example, y=x ^3

When x is smaller than 0, the graph concave downward,
when x is greater than 0, the graph concave upward
at x = 0, the concavity changes from downward to upward.
Hence x= 0 is the PI

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