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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 37RE

(a)

To determine

**To find:** The derivative of the function

Expert Solution

The derivative of

**Formula used:**

The derivative of a function *f,* denoted by

**Calculation:**

Obtain the derivative of the function

Compute

Multiply and divide

Since the limit *h* approaches zero but not equal to zero, cancel the common term *h* from both the numerator and the denominator,

Thus, the value of the derivative is

(b)

To determine

**To find:** The domain of *f* and

Expert Solution

The domain of *f* is

**Calculation:**

Obtain the domain of

Since square root is only defined for non-negative integers,

So, take

Thus, the domain of *f* is

Obtain the domain of

Since square root is only defined for non-negative integers and denominator is undefined at zero.

So, take

Thus, the domain of

**(c)**

To determine

**To check:** The answer to part (a) is reasonable by comparing the graphs of

Expert Solution

The answer to part (a) is reasonable.

**Graph:**

Use the online graphing calculator to draw the graph of

**Observation:**

From Figure 1, it is observed that the slope of the function

is always negative.

Also, the derivative graph

Thus, it can be concluded that the answer to part (a) is reasonable.