   Chapter 8.4, Problem 67E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Meteorology The normal average daily temperature in degrees Fahrenheit for a city is given by T = 55 − 21   cos   2 π ( t − 32 ) 365 where t is the time (in days), with t = 1 corresponding to January 1. Find the expected date of(a) the warmest day. (b) the coldest day.

(a)

To determine

To calculate: The expected date of the warmest day from the function of the normal average daily temperature for a city T=5521cos2π(t32)365, where t is the time in days and t=1 means January 1.

Explanation

Given Information:

The normal average daily temperature for a city is given by,

T=5521cos2π(t32)365

Where t is the time in days.

Formula used:

Cosine differentiation rule:

ddx[cosu]=sinududx

General power rule of differentiation:

ddx[xn]=nxn1

Calculation:

Consider the provided function:

T=5521cos2π(t32)365

Differentiate the above function using Cosine and general power rules of differentiation.

T=ddtddt[21cos2π(t32)365]=0((21sin2π(t32)365)(2π365))=42π365sin2π(t32)

(b)

To determine

To calculate: The expected date of the coldest day from the function of the normal average daily temperature for a city T=5521cos2π(t32)365, where t is the time in days and t=1 means January 1.

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