Point of inflection

Hi, how do i know if i am finding a point of inflection that is non stationary or stationary?

To find the point of inflection you make the 2nd derivative equal zero, right?
If its a stationary point of inflection, the first derivative will also equal zero at that point, so sub your value from d2y/dx2 into dy/dx and if it equals zero, it is statioanry, and if it isnt 0, its a non stationary point.

Reply 2

old_engineer

Original post by Emmmaaaa...

To find the point of inflection you make the 2nd derivative equal zero, right?

Not quite. At a point of inflection, the second derivative must change sign (i.e. pass through zero from positive to negative or negative to positive).

If not convinced, consider the curve y = x^4. The second derivative of that function is zero at x = 0, but it's not a point of inflection. (The curve does not change from convex to concave or vice versa).

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