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Section Assignment #9 - Done In Class 3/27

  1. Consider a function \(f(x)\) which is continuous and differentiable for all \(x\). Show that if \(f(x)\) has two roots, then \(f'(x)\) must have at least one root.
    Recall, \(r\) is a root of a function \(g\) if \(g(r)=0\).

  2. Suppose a sailboat travels 184 seamiles in a 24 hour period. Explain why at some point during this window of the the boat's speed must have exceeded 7.5 knots (seamiles per hour).