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? You should be aware that there are two different tests that may work. Either use the Second Derivative test and look at concavity at A, or use the First Derivative test and examine the sign table.
Type in your answer as LMIN, LMAX, or NEITHER.