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A continuous function, f, has domain all real numbers. If f(-1) = 5 and f(1) = -5, explain why f must have at least one zero in...Asked by Anonymous
A continuous function f has domain of all real numbers. If f(-1) = 5 and f(1) = -5, explain why function f must have at least one zero in the interval [-1, 1]
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Answered by
Steve
Because f is continuous in the specified interval, the Intermediate Value Theorem applies. It can't get from 5 to -5 without assuming every value in between. In particular, zero.
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