00:01
In this problem we are provided with a function c of t which equals to 0 .1 times t over t squared added with 40.
00:14
C of t gives the concentration of a drug t hours after the drug was administered.
00:24
So the time t is in r's over here.
00:28
We are asked to find the time when the concentration.
00:33
Of the drug is maximum.
00:39
So for this, let us find the first derivative of c of t.
00:43
So c dash of t, that is the first derivative of c of t, equals to, we do this using the quotient rule of differentiation, which is u over v, the whole dash equals to v, u dash minus u v v dash divided by v squared.
01:07
Here dash denotes the first derivative.
01:11
Since v is t squared plus 40, let us first write t squared plus 40 times the derivative of 0 .1 t is 0 .1 minus now let us write u which is 0 .1 times differentiating t squared plus 40 we get 2 t plus 0 divided by t squared plus 40 the whole squared.
01:42
Simplifying the numerator we get 0 .1 t squared plus 4 minus 0 .2 t squared divided by t squared plus 40 the whole square...