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## Homework Statement

function [tex]y(x) = x^2 + x + 1[/tex]

## The Attempt at a Solution

I count derivative: [tex]f^{\prime} (x) = 2x + 1[/tex] and now [tex]f^{\prime (x) = 0[/tex] when [tex]x=-\frac{1}{2}[/tex] and how to describe monotonic now? [tex]f(x)[/tex] is decreasing for [tex]x \in \left(- \infty; -\frac{1}{2}\right][/tex] or [tex]x \in \left(- \infty; -\frac{1}{2}\right)[/tex]? open or closed interval? and now increasing for what [tex]x[/tex]?