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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.4, Problem 56E

(a)

To determine

**To find:** The value

Expert Solution

The value

**Given:**

The function is

**Result used: Chain Rule**

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

The slope of the line passing through the points

**Calculation:**

Obtain the derivative of *.*

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

Substitute

From the given graph it is observed that,

Obtain the values

From the given graph, draw the tangent line at

Use the slope formula stated above and compute the slope of the line passing through the points

From the given graph it is observed that,

Thus, the value is

Similarly, the value

Substitute

Therefore, the value

(b)

To determine

**To find:** The value

Expert Solution

The value

**Given:**

The function is

**Calculation:**

Obtain the derivative of *.*

Let

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

The derivative of

Substitute

Thus, the derivative is

The derivative of

Thus, the derivative is

Substitute

Substitute

Obtain the value of

From the given graph, draw the tangent line at

Use the slope formula stated above and compute the slope of the line passing through the points

From the given graph observe that,

Thus, the value

Substitute 2 for

Therefore, the value