Chapter 2.6, Problem 41E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Fanciful shapes can be created by using the implicit plotting capabilities of computer algebra systems.

(a) Graph the curve with equation

At how many points does this curve have horizontal tangents? Estimate the *x*-coordinates of these points.

(b) Find equations of the tangent lines at the points (0, 1) and (0, 2).

(c) Find the exact *x*-coordinates of the points in part (a).

(d) Create even more fanciful curves by modifying the equation in part (a).

To determine

(a)

**To graph:**

The curve and find how many point have horizontal tangents and what are the x –coordinates of these points:

Explanation

The graph of given curve is

To determine

**(b)**

**To find:**

Equation of tangent lines at points (0, 1) and (0, 2)

To determine

**(c)**

**To find:**

The exact x- coordinates of points in part a)

To determine

**(d)**

**To create:**

More fanciful curves by modifying the equation

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