Question

The temperature of a patient during an illness is given by the function T = -0.1d2 + 1.2d + 98.2 where T = the patient's temperature and d = the number of days after the onset of the illness. a. On what day was the patient's temperature the highest? b. What was the patient's highest temperature?

Answer 1

a) The highest temperature was registered on the sixth day after the onset of the illness.

b) The highest temperature of the patient is 101.8.

Explanation:

Let
`T = -0.1\cdot d^(2)+1.2\cdot d +98.2`, we can find the maximum and minimum temperature of the patient by means of the First and Second Derivative Tests, whose procedure is described below:

First Derivative Test

`T' = -0.2\cdot d +1.2`

`-0.2\cdot d +1.2 = 0`

`d = 6`

Second Derivative Test

`T'' = -0.2`

Which means that critical value found in the previous step is an absolute maximum and there is no absolute minimum.

a) The highest temperature was registered on the sixth day after the onset of the illness.

b) We evaluated the function at critical value found by First Derivative Test:

`T (6) = -0.1\cdot (6)^(2)+1.2\cdot (6) +98.2`

`T(6) = 101.8`

The highest temperature of the patient is 101.8.