Question

a)Give an example of a differential function f whose first derivative is 0 at some point c even though f has neither a local maximum nor a local minimum at c.
b)How is this consistent with the theorem:
if x has a local max or min val at interior point c of it's domain and it's f' is defined at c the F'(c) = 0.

Answer 1

f(x) = x^3 at x = 0

Answer 2

@zzr0ck3r could you explain how you got that?

Answer 3

do you agree that the derivative of f(x) = x^3 is equal to 0 at x = 0?

Answer 4

yes.