00:01
For this problem, we are asked to identify the open intervals on which the function y equals negative of x plus 1 all squared is increasing or decreasing.
00:08
So the first thing that we can note here, we will be doing this using the derivative, but we can take some cues from what we know about functions.
00:15
This is a parabola because we have something squared, and we know that it has a negative leading coefficient, so it's going to be a parabola opening downwards.
00:24
As well, we can see that we'll have this is going to equal 0 when x equals negative 1, so we would expect, just without doing any calculus, basically, we'd expect that we're increasing when we're to the left of negative 1 and decreasing when we're to the right of it.
00:38
But we can verify this by taking the derivative of y with respect to x, which by application of the chain rule, we'll get that that is going to equal negative 2 of x plus 1, which will equal 0 if x equals negative 1, confirming what we saw it before.
00:56
And we can see that if we take some value to the left of that, i .e.
01:01
You know, x equals negative 2, then we'll have, oh, whoops, i got thrown across the page there...