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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.3, Problem 23E

(a)

To determine

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

Expert Solution

The equation of the tangent line to the curve

**Given:**

The equation of the curve is

**Derivative rules:**

(1) Constant Multiple Rule:

(2) Power Rule:

(3) Product Rule:

**Formula used:**

The equation of the tangent line at

where, *m* is the slope of the tangent line at

**Calculation:**

The derivative of

Apply the product rule (3),

Apply the constant multiple rule (1),

Apply the power rule (2) and simplify the expressions,

Therefore, the derivative of the function

The slope of the tangent line at

Thus, the slope of the tangent line at

Substitute *m* in equation (1),

Therefore, the equation of the tangent line to the curve

(b)

To determine

**To sketch:** The given curve and the tangent line at the given point

Expert Solution

**Given:**

The curve is

**Graph:**

Use the online graphing calculator to draw the graph of the curve and the tangent line as shown below in Figure 1.

From Figure 1, it is observed that the equation of the tangent line touches the curve