00:01
Ok, so in this exercise we have our function f of x equal to xa multiplied by 4 minus xb, defined on the interval 0 ,4.
00:13
Now, we want to find the maximum and the minimum of f on this interval, and we know that a and b are greater than 0.
00:23
How can we find the maximum and the minimum? well, we need to find the derivative of f first.
00:29
The derivative of f, thanks to the product rule, is going to be the derivative of this guy a, multiplied by 4 minus xb, plus xa multiplied by the derivative of this one, which is negative b.
00:45
So, we get 4a minus...
00:48
Oh, 4ab, because we are multiplying by b.
00:52
Perfect.
00:53
Minus abx minus abx.
00:59
And this guy here, well, this guy here can be written as ab multiplied by 4 minus 2x.
01:09
Perfect.
01:10
Ok, at this point we can draw a sine chart for f'.
01:15
Here we have 0, here we have 2, the only 0 of f', here we have 4...