00:01
So we're given these two conditions that the derivative of our function f of x is greater than 0, and the second derivative of our function f of x is less than 0 for all x.
00:11
And so what the derivative being greater than 0 means is that we're increasing for the entirety of this function, and what the second derivative being less than zero means is that we are concave down for the entirety.
00:23
So this first derivative, it always tells us if we're increasing or decreasing, second derivative tells us about concavity.
00:31
So if we're going to draw a sketch of this graph, we want a concave down graph that is always increasing.
00:39
So we're going to want a graph that looks kind of like this.
00:43
We're still concave down.
00:45
We're an upside -down u -shaped type of graph, but we never actually go decreasing.
00:55
So we never actually, it's not like a parabola, where we would come back and actually have this upside down u...