a) The curve with equation y² = x³ + 3x' Tschirnhausen cubic. Find an equation line to this curve at the point (1, –2). b) At what points does this curve have hor c) Illustrate parts (a) and (b) by graphing

a) The curve with equation y² = x³ + 3x' Tschirnhausen cubic. Find an equation line to this curve at the point (1, –2). b) At what points does this curve have hor c) Illustrate parts (a) and (b) by graphing

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 43E

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Question

3.
(a) The curve with equation y² = x³ + 3x² is called the
Tschirnhausen cubic. Find an equation of the tangent
line to this curve at the point (1, –2).
(b) At what points does this curve have horizontal tangents?
(c) Illustrate parts (a) and (b) by graphing the curve and the
tangent lines on a common screen.

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