The function $x ( \alpha - x )$ is strictly increasing on the interval $0 < x < 1$ if and only if (a) $\alpha \geq 2$ (b) $\alpha < 2$ (c) $\alpha < - 1$ (d) $\alpha > 2$.
(a) Differentiate.
The function $x ( \alpha - x )$ is strictly increasing on the interval $0 < x < 1$ if and only if\\
(a) $\alpha \geq 2$\\
(b) $\alpha < 2$\\
(c) $\alpha < - 1$\\
(d) $\alpha > 2$.