Question

If f'(x)=0 at each x of an open interval (a,b), then f(x)=C is a constant for all x in (a,b)

true or false?

can you explain why as well?

Answer 1

f'(x) is the slope of tangent at all points in (a,b) so the graph is a horizontal line so f(x) is a constant C

Answer 2

so true.

Answer 3

yes