Question

Suppose that y=f(x) has a maximum at x=x_0. The value of the first order derivative evaluated at this point, i.e. f'(x_0), will be:
a)zero
b)positive
c) negative
d) it is not possible to tell. It could be positive, negative or equal to zero

Answer 1

Fermat's Theorem:

If f(x) has a local maximum or a local minimum at x = c, and if f '(c) exists, then f '(c) = 0.

There the answer to your question is A).

Does that help.

Answer 2

yes, thanks

Answer 3

You're welcome.