# Monotonic function

player1_1_1

## Homework Statement

function $$y(x) = x^2 + x + 1$$

## The Attempt at a Solution

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

Homework Helper
i'd say two open intervals
f(x) is decreasing for $x \in \left(- \infty, -\frac{1}{2}\right)$
f(x) is increasing for $x \in \left(-\frac{1}{2}\right, \infty \right)$

and neither at $x = -\frac{1}{2}$

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