MathCastle
Multivariable CalculusHardThe Chain Rule & Implicit Differentiation

The Chain Rule & Implicit Differentiation · Hard problem

An indifference curve for a consumer satisfies xy=12xy=12 (constant utility), passing through (3,4)(3,4). Use a quadratic (second-order Taylor) approximation, based on y′y' and y′′y'' found by implicit differentiation at x=3x=3, to estimate yy when x=3.3x=3.3.