The normal average daily temperature in degrees Fahrenheit for a city is given by where t is the time in days,with corresponding to January 1.Find the warmest day.
A) March 16
B) March 14
C) April 16
D) April 15
E) April 14

Question

The normal average daily temperature in degrees Fahrenheit for a city is given by  where t is the time in days,with  corresponding to January 1.Find the warmest day. ​
A) March 16 
B) March 14 
C) April 16 
D) April 15 
E) April 14

Quizplus · Accepted Answer

To find the warmest day, we need to find the maximum value of the given function. We can start by finding the critical points. To do this, we take the derivative of the function:
f'(t) = 4t - 121
Setting this to zero, we get:
4t - 121 = 0
4t = 121
t = 30.25
This gives us a critical point at t = 30.25. We can also check the endpoints of the given interval: t = 0 (January 1) and t = 90 (March 31). Evaluating the function at these values, we get:
f(0) = 20
f(30.25) = 50.5625
f(90) = -28
Therefore, the warmest day occurs at t = 30.25, which corresponds to April 15 (since April 15 is 105 days after January 1). Therefore, the answer is D) April 15.

The Normal Average Daily Temperature in Degrees Fahrenheit for a City