Math Problem Statement
determine the equation of thr tangent to the curve x cubed +2xysquared +ycubed -21 =0 at point 1,2
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Tangent Line
Derivatives
Algebraic Curves
Formulas
Implicit differentiation: d/dx[f(x, y)] = 0
Slope of the tangent: dy/dx = - (∂f/∂x) / (∂f/∂y)
Point-slope form: y - y1 = m(x - x1)
Theorems
Implicit Differentiation Theorem
Suitable Grade Level
Grades 10-12
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