00:01
In this problem, we are given with a of t, which gives the activity level of a certain type of lizard at a particular time, say t, where t denotes the number of hours after 12 noon.
00:18
A of t is given by 0 .008 times t cube minus 0 .283 t squared plus 0 .283 t squared plus 0.
00:32
2 .304 t plus 3.
00:38
We are as to find when this function reaches the maximum value and when it reaches the minimum value.
00:49
To find that first we need to find the critical point of the given function.
00:55
That is, we need to find the point when the value of a dash of t reaches zero.
01:02
Let's just say, c is our critical point.
01:06
After finding the critical point, we need to find the value of a double dash of c.
01:13
If a double dash of c comes as less than zero, then we can say at t is equal to c, the function a of t reaches maximum.
01:28
If a double dash of c comes as positive, then we can say at t is equal to c, the function a of t reaches minimum.
01:41
Let's do that one by one.
01:44
First, we are going to compute the value of a dash of t.
01:47
It will be equal to 0 .024 times t squared minus 0 .5 -6 times t times t.
01:59
Plus 2 .304.
02:04
If we equate this expression to 0 and solve for t, we will get t is equal to 283 plus or minus root of 24793 divided by 24.
02:22
Or we can say t can be approximated as 18 .35 and 5 .5.
02:30
To 3.
02:32
Now we need to compute the value of a double dash of t at t is equal to these two values...