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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.3, Problem 38E

(a)

To determine

**To find:** The rate of change of *F* with respect to

Expert Solution

The rate of change of *F* with respect to

**Given:**

The magnitute of the force is

Where, *W* is weight.

**Derivative Rule: Quotient Rule**

If

**Calculation:**

Obtain the derivative of *F.*

Apply Quotient Rule as shown equation (1),

Therefore, the rate of change of *F* with respect to

(b)

To determine

**To find:** The value of

Expert Solution

The rate of change equal to zero when

**Given:**

From part (a), the rate of change of *F* with respect to

**Calculation:**

The rate of change equal to zero,

Since

Therefore, the rate of change equal to zero when

(c)

To determine

**To draw:**. The graph of *F* as a function of

Expert Solution

**Given:**

The magnitute of the force is

Use online graphing calculator to draw the graph of *F* as a function of

The value of

**Calculation:**

Obtain the magnitute of the force *F* as a function of

Substitute

Therefore, the magnitute of the force *F* as a function of

From part (b), the rate of change equal to zero when

Substitute

Therefore, the value of

Substitute *F.*

Therefore, the point

Use online graphing calculator and draw the graph of *F* as a function of

From Figure 1, it is observed that the slope of tangent is horizontanl to the curve

Hence, the value of