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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 3.1, Problem 76E

(a)

To determine

**To evaluate:** The function that models the cross section area of gutter in terms of

Expert Solution

The function that models area of gutter is

**Given:**

A rain gutter is formed by bending up the side of

**Calculation:**

The width of the gutter is

The length of the corral is

The area of the gutter is,

From the equation (1)

The area of gutter in the term of

Thus, the function that models area of gutter is

(b)

To determine

**To evaluate:** The value of

Expert Solution

The value of

**Given:**

A rain gutter is formed by bending up the side of

**Calculation:**

The width of the gutter is

The length of the corral is

The area of the gutter is,

From the equation (1),

The area of gutter in the term of

The standard form of function,

The maximum or minimum value of the function occurs at,

If

If

From the equation (3) and (4),

Substitute

The value of

The function has maximum value,

Thus, the value of

(c)

To determine

**To evaluate:** The maximum cross-sectional area of the gutter.

Expert Solution

The maximum cross sectional area of the gutter is

**Given:**

A rain gutter is formed by bending up the side of

**Calculation:**

The width of the gutter is

The length of the corral is

The area of the gutter is,

From the equation (1)

The area of gutter in the term of

The standard form of function,

The maximum or minimum value of the function occurs at,

If

If

From the equation (3) and (4),

Substitute

The value of

The function has maximum value,

Substitute

The maximum cross sectional area of the gutter is

Thus, the maximum cross sectional area of the gutter is