00:01
We're taking a look at a function.
00:04
Let's go ahead and start by calculating the derivative of the function.
00:09
So first, we're going to do a power rule, and then we have 2e to the x, and now notice that this thing is always greater than zero.
00:28
So that tells us that f is strictly increasing.
00:35
Okay, when the derivative is always positive, that tells us that f is strictly increasing.
00:42
And if f is strictly increasing, that tells us f is one to one.
00:47
Okay, so that's it for part a.
00:50
Oh, i guess we also need to calculate f at zero.
00:54
So we plug it in, we get zero plus two times one, that's two.
00:59
Okay, now let's go ahead and do part b...