00:01
We will sketch the graph of the function exponential of x and use that graph to find the absolute local, maximum and minimum values of the function.
00:13
So we know that this exponential function is equal to 1 at 0.
00:20
It is increasing, always increasing, it is always positive, it increases quickly, and when x is large but negative, that is, if we move on the graph to the left, to negative infinity, the values that function are closer and closer to zero, but always positive.
00:44
It means that the graph of this function is more or less like this.
00:50
We have an asymptotic behavior to the left, and then we have an rapidly increasing behavior to the right.
01:03
Here we have the value 1 at 0.
01:08
So this is more or less the graph, the exponential function.
01:12
And we see clearly here that limit when x goes to plus infinity of the function is plus infinity, it means the function grows without any bound when x is large and positive.
01:30
It means the graph goes up...