Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.6, Problem 9E

**(a)**

To determine

**To find:** The slope of the tangent line to the curve.

Expert Solution

The slope of the tangent line to the curve

**Given:**

The equation of the curve is

The curve passing through the points (1, 5) and (2, 3).

**Formula used:**

The slope of the tangent curve

**Calculation:**

Obtain the slope of the tangent to the curve at the point

Since

Perform the mathematical operations as shown below.

Since the limit *h* approaches 0 but not equal to 1, cancel the common term

Thus, the slope of the tangent line to the curve at the point

**(b)**

To determine

**To find:** The equation of the tangent lines to the curve

Expert Solution

The equation of the tangent lines to the curve

(2, 3) are

**Formula used:**

The equation of the tangent line to the curve

Since the tangent line to the curve *a,* the value of

At the point (1, 5), take

Substitute

Isolate *y* as shown below:

Thus, the equation of the tangent line is

Obtain the equation of the tangent line at the point (2, 3).

Since the tangent line to the curve *a,* the value of

At the point (2, 3), take

Substitute

Isolate *y* as shown below:

Thus, the equation of the tangent line is

**(c)**

To determine

**To sketch**: The graph of the curve and the tangent lines.

Expert Solution

**Given:**

The equation of the curve is

The equation of the tangent lines are

**Graph:**

Use the online graphing calculator to draw the graph of the functions as shown below in Figure 1.

Notice that, the two lines