Please indicate if each statement is true or false and if false please explain why
If f'(x) = 0 for all of x in the domain of f, then f is a constant function.
If the graph of a function has three x intercepts, then it must have at least two points at which its tangent line is horizontal.
Response: If you draw a simple "curved" function that intercepts the x-axis three times, you will find that it has two "humps." One hump looks like an upside down "U" ...
This is a proof regarding the intercepts and horizontal tangent lines of a function.