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?

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.

Step-by-step explanation:

Let , 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

Second Derivative Test

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:

The highest temperature of the patient is 101.8.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.