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 10E

(a)

To determine

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

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, 1) and

**Formula used:**

The slope of the tangent curve

**Difference of square formula:**

**Calculation:**

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

Since

Multiply both the numerator and the denominator by the conjugate of the numerator.

Apply the difference of squares formula,

Since the limit *x* approaches to *a* but not equal to *a*, cancel the common term

Perform the mathematical operations and compute the value of the function as shown below.

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 at the given points.

Expert Solution

The equation of the tangent lines to the curve

**Formula used:**

The equation of the tangent line to the curve

**Calculation:**

Obtain the equation of the tangent line at the point (1, 1).

Since the tangent line to the curve *a*,

At the point (1, 1), consider

Substitute

Isolate *y* as shown below:

Thus, the equation of the tangent line is

Obtain the equation of the tangent line at the point

Since the tangent line to the curve *a*,

At the point

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.

From Figure 1, it is noticed that the two lines