00:01
In this question, we're given the temperature t of a patient.
00:04
It's related to the dosage given to the patient.
00:09
The dosage is in d.
00:12
Now, c is a constant.
00:14
We want to find the value of d where t is maximum, where the temperature is maximum.
00:28
And next, we were given that sensitivity is defined to be the t over dd.
00:39
And want to find d when sensitivity is maximum.
00:51
Alright, let's look at the, let's expand out.
00:59
We will get c over 2d square minus d cubed over 3.
01:06
Now, let's differentiate temperature respect to d.
01:11
We'll get c over 2.
01:14
D square, when you differentiate, you get 2d, minus 1 3d d cubed when you differentiate you get 3d square so this gives us the differentiation is can cancel this off is cd minus d square now we're going to set the differentiation to 0 so we get cd minus d square equals to 0 factorize out the d you get this so you get d equals zero or d equals to c.
01:59
Now, you will reject zero dosage because that's not what we're looking for.
02:05
So this equals to c.
02:06
Now, we need to investigate whether this will give maximum t.
02:11
So let's look at the second order differentiation.
02:16
So that means we differentiate one more time from here...