Question

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

Answer 1

`F(x)` is strictly increasing for any `m in RR`...

Explanation:

Note that:

`m^2+m+1 = m^2+2(1/2)m+1/4+3/4`

`color(white)(m^2+m+1) = (m+1/2)^2+3/4 >= 3/4` for any `m in RR`

Hence `F(x)` is the equation of a line with positive slope, thus strictly increasing.