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Part of 2022 ISI Entrance Examination

Problems(1)

B.Stat & B.Math 2022 - Q2

Source: Indian Statistical Institute (ISI) - B.Stat & B.Math Entrance 2022

5/8/2022
Consider the function f(x)=∑k=1m(x−k)4 , x∈Rf(x)=\sum_{k=1}^{m}(x-k)^{4}~, \qquad~ x \in \mathbb{R} where m>1m>1 is an integer. Show that ff has a unique minimum and find the point where the minimum is attained.
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