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). y = (b) At what points does this curve have horizontal tangents? (x,y) ( ) smaller y value (x,y) ( ) larger y value

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). y = (b) At what points does this curve have horizontal tangents? (x,y) ( ) smaller y value (x,y) ( ) larger y value

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Question

(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). y =

(b) At what points does this curve have horizontal tangents?

(x,y) ( ) smaller y value

(x,y) ( ) larger y value

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