Abstract
InR 1, if a continuous function has opposite signs at the endpoints of an interval, then the function has a zero in the interval. If the function has a nonvanishing derivative at a zero, then there is an interval such that the function has opposite signs at the endpoints. In this paper each of these results is extended toR n.
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The research of this author has been partially supported by ONR Contract N000-14-67-A-0285-0019 (NR #047-095) and by NSF Contract SOC-7402516.
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Gould, F.J., Tolle, J.W. An existence theorem for solutions tof(x) = 0. Mathematical Programming 11, 252–262 (1976). https://doi.org/10.1007/BF01580394
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DOI: https://doi.org/10.1007/BF01580394