00:01
In this problem we have to find the absolute maximum and absolute minimum values of f on the given interval.
00:08
So function f is here, fx equal x plus 4x.
00:16
And the given interval is 0 .2 comma 8.
00:20
So before finding the local maximum and local minimum, first we will find the functional value or the function value at the end point of this interval.
00:31
So first we will find f of 0 .2.
00:35
This is equal to 0 .2 plus 4 by 0 .2, that is 0 .2 plus 20.
00:43
So f of 0 .2 is equal 20 .2.
00:49
And the second, f of 8, that is 8 plus 4 by 8.
00:58
So this is equal to f8 is 8 .5.
01:02
Now to check the local maximum and local minimum we will find the critical numbers are the critical points.
01:16
Let's say find critical numbers of fx.
01:22
That is the values of x at which f dash x equal 0.
01:28
So we will have here f dash x.
01:31
So writing f dash x equal d by d x of x plus 4x.
01:39
So this is equal to 1 minus 4 by x square.
01:44
F test x is equal 1 minus 4 by x square...