a. Find equations of the tangent and normal line to the curve y = In(x² – 2x + 2) at x=2. b. Plot the graph of the function, together with the tangent and normal curve to verify your result. c. Describe the trajectory of the normal curve with respect to the tangent line.

a. Find equations of the tangent and normal line to the curve y = In(x² – 2x + 2) at x=2. b. Plot the graph of the function, together with the tangent and normal curve to verify your result. c. Describe the trajectory of the normal curve with respect to the tangent line.

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

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a. Find equations of the tangent and normal line to the curve y = In(x² – 2x + 2) at
x=2.
b. Plot the graph of the function, together with the tangent and normal curve to verify
your result.
c. Describe the trajectory of the normal curve with respect to the tangent line.

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