Calculus

Give an example of a function with a critical point that is neither a maximum nor a minimum. Specify the relevant point(s).

This is what I have and this is what I got wrong...

A function with a critical point that is neither a maximum nor a minimum would be f(x)=x^2 if F(x) = x^ 2 , x ∈ (−∞, 0) ∪ (0, ∞) then it would have no local/ absolute minimum and no local/absolute maximum.

Can anyone explain to me why this is wrong?? And can I get an example of what IS right!

Thank you!

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  1. how about the good old f(x) = x^3

    at x=0, f'=0, but it is an inflection point.

    the problem with your function is that f(0) is not even defined!

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  2. f(x) = x^2 has a critical point (and a MINIMUM) at x=0

    f(x) = (x^3 + 3x^2 - 4x - 12) / (x+2)
    ... has a critical point (and a "hole" at x=-2)

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