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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.4, Problem 72E

To determine

**To find:** The number of hours of daylight increases in Philadelphia on March 21 and May 21.

Expert Solution

The number of hours of daylight increases in Philadelphia on March 21 and May 21 is approximately 0.0482 and 0.02398.

**Given:**

The function

**Derivative rule:**

(1) *Constant Multiple Rule*:

(2) *Sum Rule*:

(3) *Quotient Rule*:

**Result used:** Chain Rule

If *g* is differentiable at *x* and *f* is differentiable at *x* and

**Calculation:**

Obtain the derivative of

Apply the sum rule (1) and the constant multiple rule (2),

Apply the chain rule as shown in equation (1),

Let

The derivative of

Substitute

Thus, the derivative is

The derivative of

Thus, the derivative is

Substitute

Therefore, the derivative is

Given that, the rate of the length of daylight is increasing in Philadelphia on March 21 and May 21. That is,

Obtain the value of *t* for which

Note that,

Here, *t* is from 21st March to 20^{ }th June.

On March 21, the value of

Substitute

Thus, the number of hours of daylight is increasing in Philadelphia on March 21 is approximately 0.0482.

On May 21, the value of *t* is

Substitute

Thus, the number of hours of daylight increases in Philadelphia May 21 is approximately 0.02398.

**Note:**