Consider the function $f(x) = -4 x^2 + 4 x - 3$. $f(x)$ is increasing on the interval $(-\infty, A]$ and decreasing on the interval $[A,\infty)$ where $A$ is the critical number.
Find $A$
At $x = A$, does $f(x)$ have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.