Interval Notation for Increasing and Decreasing Intervals of a FunctionThis was brought up by another student in one of my pre-calculus classes.The graph was a simple quadratic x 2 . The teacher stated that the graph was decreasing from ( − ∞ , 0 ), and increasing from ( 0 , ∞ ).Why would zero not be included? i.e: decr. ( − ∞ , 0 ] and incr. [ 0 , ∞ )

Question

Interval Notation for Increasing and Decreasing Intervals of a FunctionThis was brought up by another student in one of my pre-calculus classes.The graph was a simple quadratic       x    2  . The teacher stated that the graph was decreasing from   (  −  ∞  ,  0  ), and increasing from   (  0  ,  ∞  ).Why would zero not be included? i.e: decr.   (  −  ∞  ,  0  ] and incr.   [  0  ,  ∞  )

reinmelk3iu · Accepted Answer

Explanation:Because for f(x) to be decreasing       f    ′    (  x  )  &amp;lt;  0. And for increasing       f    ′    (  x  )  &amp;gt;  0. But at   x  =  0,       f    ′    (  x  )  =  0 hence it&#039;s neither decreasing nor increasing at   x  =  0

figoveck38 · Accepted Answer

Explanation:Generally the 0 is not included because the function is not decreasing (or increasing) at 0.It would be accurate, however to say that   y  =      x    2   is non-increasing on the interval   (  −  ∞  ,  0  ]