Math Problem Statement

Determine the equations of the tangent and normal lines at P(1,1) given by x^3y - 2xy^2 + x^2 -3y +3 =0

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Implicit Differentiation
Tangents and Normals

Formulas

Implicit differentiation: d/dx(f(x, y) = 0)
Slope of tangent line: dy/dx
Equation of tangent line: y = mx + b
Equation of normal line: y = -1/m(x - x1) + y1

Theorems

Product Rule
Chain Rule

Suitable Grade Level

Grades 11-12