Mathematics

Mathematics

Problem

The second derivative of a family of functions is given by fk′′(x)=ke−x2−1f_k''(x)=k e^{-x^{2}}-1, where kk is a real parameter. For which of the following is the corresponding function concave down on its entire domain? a) 0<k<10<k<1 b) k<1k<1 c) k≤1k\le 1 d) k>1k>1

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