This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 3

2018 VTRMC, 6
Tags: VTRMC , college contests , Sequences , extrema , maximum , minimum value
For $n \in \mathbb{N}$, define $a_n = \frac{1 + 1/3 + 1/5 + \dots + 1/(2n-1)}{n+1}$ and $b_n = \frac{1/2 + 1/4 + 1/6 + \dots + 1/(2n)}{n}$. Find the maximum and minimum of $a_n - b_n$ for $1 \leq n \leq 999$.

1986 Traian Lălescu, 1.3
Tags: algebra , Polynom , extrema , supremum , polynomial function , real analysis
Let be four real numbers. Find the polynom of least degree such that two of these numbers are some locally extreme values, and the other two are the respective points of local extrema.

2007 Mathematics for Its Sake, 1
Tags: function , real analysis , extrema , differentiability
Find the number of extrema of the function $ f:\mathbb{R}\longrightarrow\mathbb{R} $ defined as $$ f(x)=\prod_{j=1}^n (x-j)^j, $$ where $ n $ is a natural number.