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 5E

To determine

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

Expert Solution

The equation of the tangent line to the curve

**Given:**

The equation of the curve is

The curve passing through the point

**Formula used:**

The slope of the tangent curve

The equation of the tangent line to the curve

**Calculation:**

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

Substitute

The factors of

Thus, the slope of the tangent line to the curve becomes,

Since the limit *x* approaches 2 but not equal to 2, cancel the common term

Thus, the slope of the tangent line to the curve at the point (2, −4) is,

Obtain the equation of the tangent line.

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

Substitute

Isolate *y* as shown below.

Thus, the equation of the tangent line is