Solve the problem of maximizing 10x — x^2 subject to x — ɑ ≤ 0, ɑ ϵ R. Determine the maximum value function.
ɑ = alpha
Draw a graph of $\displaystyle f(x) = 10x - x^2$.
Then you should see that if $\displaystyle \alpha \leq 5$ the maximum value is $\displaystyle f(\alpha)$ and if $\displaystyle \alpha > 5$ the maximum value is $\displaystyle f(5)$.