00:01
Now here in this question, we look at two functions, right? and the first one has a function is given by fx equals 3x2 for 3 minus 2x, right? so you also define the minimum and maximum value of the function on the interval x minus 1 to 1.
00:17
So to do that, of course, first i would like to look at the, i would look at the, i would look at the derivative of this function, fx derivative.
00:31
Given by, i was given by two times x minus one over three minus two, right? and so that's two over x, one over cubic load and over two, right? so it's very clear that when x small and this is positive, but when x is very large and then becomes negative, right? so it's good to actually sketch this function of x versus is very clear that when x equals zero, you get zero, right? and then when x, when x is negative, when x becomes negative, what's going to happen.
01:08
And this value will be negative.
01:10
So this will be negative.
01:11
So it's going to decrease, right? because when x is negative, when x is negative, actually, this is going to actually decrease.
01:19
Because this is, and very clearly, this is going to be negative value, right? so it's going to decrease.
01:24
So it will decrease, it will be decrease something like this, right? it will all the time decrease from minus 1 to 1.
01:30
And look at the one and the positive part.
01:32
You read the positive part, it depends on the value of x, right? so it's very clear that if x, if x is less than one, and then this is always less than one as well...