Question

Suppose that ​f(2​)=4 and that =0 for all x. must ​f(x)=4 for all​ x? give reasons for your answer.

Answer 1

Yes. If f'(x) = 0 everywhere, then the graph of f(x) is a horizontal line.

If f(2) = 4, then f(x) = 4 for any x.