Please indicate if each statement is true or false and if false please explain why

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.

If f'(x) = 0 for all of x in the domain of f, then f is a constant function.

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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" ...

Solution Summary

This is a proof regarding the intercepts and horizontal tangent lines of a function.

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