# Interval Notation of the Increasing and Decreasing Sections of a Quadratic

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

"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 $$x = 0.5$$.
• To clarify (just in case you haven't encountered calculus), the derivative of a function is just its slope. The slope at $x=0.5$ is $0$, that is, the function is flat at that x-value, therefore, it is neither increasing nor decreasing. It is the point of change between increasing and decreasing. – Christopher Marley Nov 5 '18 at 2:58