Interval Notation of the Increasing and Decreasing Sections of a Quadratic

Question

This is the quadratic y=-4x^2+4x+3.

Here is the graph.

I know that the increase and the decrease of a graph has to do with the y value.

From this, I know that from negative infinity to 0.5, the function is increasing. From 0.5 to positive infinity the graph is decreasing.

In interval notation Increase: (-infinity, 0.5) Decrease: (0.5, infinity) I was wondering if the bracket on the 0.5 is a square bracket or parentheses.

Thanks

Answer 1

"Increasing" or "decreasing" refer typically to having a positive or negative derivative respectively. In that light, it should be clear that $y'(0.5) = 0$ - i.e. neither positive nor negative, so at $x = 0.5$, $y$ is neither increasing or decreasing.

Therefore, the appropriate notation would be with the parentheses, i.e. $(-\infty,0.5)$ and $(0.5,\infty)$, since you don't want to include $x = 0.5$.