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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.5, Problem 29E

(a)

To determine

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

Expert Solution

The equation of the tangent line to the equation

**Given:**

The curve with equation

The point is

**Derivative rules:**

(1) Chain rule: If

(2) Product rule: If

**Formula used:**

The equation of the tangent line at

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

**Calculation:**

Obtain the equation of tangent line to the given point.

Differentiate the above equation implicitly with respect to *x*,

Apply the chain rule (1) and simplify the terms,

Therefore, the derivative of the equation is

The slope of the tangent line at

Thus, the slope of the tangent line at

Substitute

Therefore, the equation of the tangent line to the equation

(b)

To determine

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

Expert Solution

**Graph:**

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

From Figure 1, it is observed that the line