# For what values of m is F(x) = (m^2+m+1)x increasing or decreasing?

Jan 22, 2017

$F \left(x\right)$ is strictly increasing for any $m \in \mathbb{R}$...

#### Explanation:

Note that:

${m}^{2} + m + 1 = {m}^{2} + 2 \left(\frac{1}{2}\right) m + \frac{1}{4} + \frac{3}{4}$

$\textcolor{w h i t e}{{m}^{2} + m + 1} = {\left(m + \frac{1}{2}\right)}^{2} + \frac{3}{4} \ge \frac{3}{4}$ for any $m \in \mathbb{R}$

Hence $F \left(x\right)$ is the equation of a line with positive slope, thus strictly increasing.