00:01
So let us start with the concept which we are going to use here for this question for absolute extrema we have to see the f dash of x and we are need to equate x to 0 so that we will get the critical point then we can find its absolute extremas.
00:18
So for that d by dx any uh sine of ax this should be equals to you remember a cosine of ax this is what the formula of derivative.
00:32
So according to the question we have given the function f of x is equals to sine of 4x in the closed interval of 0 to pi.
00:45
So first of all let us find the f dash of x this will be goes to according to formula 4 cosine of 4x.
00:52
So let's equate f dash of x to 0 so that we will get the critical point.
00:59
So we get 4 cosine of 4x is equals to 0 this implies that cosine of 4x is equals to 0 this means to say 4x is equals to cosine inverse of 0.
01:14
So cosine inverse of 0 is only possible when 4x will be goes to pi by 2 comma 3 pi by 2 means pi by 2 multiples 5 pi by 2 comma 7 pi by 2 let's take 4 to that side so it will become pi by 4 to the 8 comma 3 pi by 8 comma 5 pi by 8 comma 7 pi by 8.
01:45
So these are the required corresponding values at which it can be minimum or maximum.
01:50
So let's check it out whether it is minimum maximum.
01:54
So we need to find the values f of 0 f of pi by 8 f of 3 pi by 8 f of 5 pi by 8 f of 7 pi by 8 and finally f of pi.
02:14
So let's find f of 0 this should be equals to sine of 4 into 0 will become 0 then f of pi by 8 this will be equals to sine of 4 pi by 8 means sine pi by 2...