If f'(x)=0, no sign change at x, then f has pt of inflection

[nikolany]

We know that if f'(x)=0 and f' does not change sign at x then f has a point of inflexion at x. I need to give an example to show that this is not always true.

Thank you

 

[stapel]

We know that if f'(x)=0 and f' does not change sign at x then f has a point of inflexion at x. I need to give an example to show that this is not always true.

If "we know" that it is true, then how are you supposed to arrive at a counter-example...? :shock:

Please reply with clarification, including your work and reasoning so far. Thank you, Alex Hall!

Eliz.

 

[daon]

f(x) = x, if x < 0.
f(x) = x^2, if 0<=x<1
f(x) = x, x>=1

f'(x)>=0 for all x.
there is no inflexion change at 0.
f'(0)=0.

edited to fix mistake.