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