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Application of Rolle's theorem - Intercepts

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Please state whether the statements are true or false, and if false, why.

If the graph of a function has three x intercepts, then it must have at least two points at whch its tangent line is horizontal.

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

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Solution Summary

This solution explains the connection between the number of x-intercepts and horizontal tangents.

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Suppose the graph has three x intercepts (assuming that the graph has amooth and no holes in it. in other words, the function is continuous and differentiable) which means the graph is cutting the x-axis in four points ...

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